<> 500 500 611.1 500 277.8 833.3 750 833.3 416.7 666.7 666.7 777.8 777.8 444.4 444.4 The comparison of the frequency of the first pendulum (f1) to the second pendulum (f2) : 2. 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 706.4 938.5 877 781.8 754 843.3 815.5 877 815.5 << /Subtype/Type1 But the median is also appropriate for this problem (gtilde). Otherwise, the mass of the object and the initial angle does not impact the period of the simple pendulum. /Name/F3 In the late 17th century, the the length of a seconds pendulum was proposed as a potential unit definition. 44 0 obj /BaseFont/JOREEP+CMR9 /Name/F5 36 0 obj /Type/Font Problem (2): Find the length of a pendulum that has a period of 3 seconds then find its frequency. 656.3 625 625 937.5 937.5 312.5 343.8 562.5 562.5 562.5 562.5 562.5 849.5 500 574.1 and you must attribute OpenStax. >> 2 0 obj Problem (12): If the frequency of a 69-cm-long pendulum is 0.601 Hz, what is the value of the acceleration of gravity $g$ at that location? 33 0 obj Pendulum 2 has a bob with a mass of 100 kg100 kg. >> The period of a simple pendulum with large angle is presented; a comparison has been carried out between the analytical solution and the numerical integration results. /LastChar 196 Put these information into the equation of frequency of pendulum and solve for the unknown $g$ as below \begin{align*} g&=(2\pi f)^2 \ell \\&=(2\pi\times 0.841)^2(0.35)\\&=9.780\quad {\rm m/s^2}\end{align*}. (* !>~I33gf. N xnO=ll pmlkxQ(ao?7 f7|Y6:t{qOBe>`f (d;akrkCz7x/e|+v7}Ax^G>G8]S n%[SMf#lxqS> :1|%8pv(H1nb M_Z}vn_b{u= ~; sp AHs!X ,c\zn3p_>/3s]Ec]|>?KNpq n(Jh!c~D:a?FY29hAy&\/|rp-FgGk+[Io\)?gt8.Qs#pxv[PVfn=x6QM[ W3*5"OcZn\G B$ XGdO[. The pennies are not added to the pendulum bob (it's moving too fast for the pennies to stay on), but are instead placed on a small platform not far from the point of suspension. <> stream Arc length and sector area worksheet (with answer key) Find the arc length. That's a gain of 3084s every 30days also close to an hour (51:24). Now, if we can show that the restoring force is directly proportional to the displacement, then we have a simple harmonic oscillator. Simple pendulum ; Solution of pendulum equation ; Period of pendulum ; Real pendulum ; Driven pendulum ; Rocking pendulum ; Pumping swing ; Dyer model ; Electric circuits; >> /FontDescriptor 8 0 R WebThe essence of solving nonlinear problems and the differences and relations of linear and nonlinear problems are also simply discussed. Problem (9): Of simple pendulum can be used to measure gravitational acceleration. That's a loss of 3524s every 30days nearly an hour (58:44). 277.8 500] << /BaseFont/EUKAKP+CMR8 /FirstChar 33 Problem (8): A pendulum has a period of $1.7\,{\rm s}$ on Earth. endobj sin Attach a small object of high density to the end of the string (for example, a metal nut or a car key). 500 500 500 500 500 500 500 500 500 500 500 277.8 277.8 277.8 777.8 472.2 472.2 777.8 Ze}jUcie[. 1 0 obj /Name/F2 [4.28 s] 4. .p`t]>+b1Ky>%0HCW,8D/!Y6waldaZy_u1_?0-5D#0>#gb? A classroom full of students performed a simple pendulum experiment. /FirstChar 33 Websome mistakes made by physics teachers who retake models texts to solve the pendulum problem, and finally, we propose the right solution for the problem fashioned as on Tipler-Mosca text (2010). Physics 1: Algebra-Based If you are giving the regularly scheduled exam, say: It is Tuesday afternoon, May 3, and you will be taking the AP Physics 1: Algebra-Based Exam. 0 0 0 0 0 0 0 0 0 0 0 0 675.9 937.5 875 787 750 879.6 812.5 875 812.5 875 0 0 812.5 What would be the period of a 0.75 m long pendulum on the Moon (g = 1.62 m/s2)? If the length of a pendulum is precisely known, it can actually be used to measure the acceleration due to gravity. 29. /Widths[285.5 513.9 856.5 513.9 856.5 799.4 285.5 399.7 399.7 513.9 799.4 285.5 342.6 /Annots [<>>> <>>> <>>> <>>> <>>> <> <> <> <> <> <> <> <> <> <> <> <> <> <> <> <>] if(typeof ez_ad_units != 'undefined'){ez_ad_units.push([[300,250],'physexams_com-leader-2','ezslot_9',117,'0','0'])};__ez_fad_position('div-gpt-ad-physexams_com-leader-2-0'); Recall that the period of a pendulum is proportional to the inverse of the gravitational acceleration, namely $T \propto 1/\sqrt{g}$. ))NzX2F <> Determine the comparison of the frequency of the first pendulum to the second pendulum. Problem (7): There are two pendulums with the following specifications. /BaseFont/NLTARL+CMTI10 Students calculate the potential energy of the pendulum and predict how fast it will travel. Example Pendulum Problems: A. When we discuss damping in Section 1.2, we will nd that the motion is somewhat sinusoidal, but with an important modication. endobj /Widths[323.4 569.4 938.5 569.4 938.5 877 323.4 446.4 446.4 569.4 877 323.4 384.9 500 500 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 625 833.3 (a) Find the frequency (b) the period and (d) its length. << This shortens the effective length of the pendulum. /Length 2736 % 275 1000 666.7 666.7 888.9 888.9 0 0 555.6 555.6 666.7 500 722.2 722.2 777.8 777.8 We can solve T=2LgT=2Lg for gg, assuming only that the angle of deflection is less than 1515. 875 531.3 531.3 875 849.5 799.8 812.5 862.3 738.4 707.2 884.3 879.6 419 581 880.8 843.3 507.9 569.4 815.5 877 569.4 1013.9 1136.9 877 323.4 569.4] Except where otherwise noted, textbooks on this site /LastChar 196 xcbd`g`b``8 "w ql6A$7d s"2Z RQ#"egMf`~$ O WebView Potential_and_Kinetic_Energy_Brainpop. For the next question you are given the angle at the centre, 98 degrees, and the arc length, 10cm. SP015 Pre-Lab Module Answer 8. 874 706.4 1027.8 843.3 877 767.9 877 829.4 631 815.5 843.3 843.3 1150.8 843.3 843.3 708.3 795.8 767.4 826.4 767.4 826.4 0 0 767.4 619.8 590.3 590.3 885.4 885.4 295.1 Representative solution behavior and phase line for y = y y2. 708.3 795.8 767.4 826.4 767.4 826.4 0 0 767.4 619.8 590.3 590.3 885.4 885.4 295.1 277.8 500] The equation of frequency of the simple pendulum : f = frequency, g = acceleration due to gravity, l = the length of cord. endobj 351.8 935.2 578.7 578.7 935.2 896.3 850.9 870.4 915.7 818.5 786.1 941.7 896.3 442.6 777.8 777.8 1000 1000 777.8 777.8 1000 777.8] 571 285.5 314 542.4 285.5 856.5 571 513.9 571 542.4 402 405.4 399.7 571 542.4 742.3 >> /Name/F6 Examples of Projectile Motion 1. Given: Length of pendulum = l = 1 m, mass of bob = m = 10 g = 0.010 kg, amplitude = a = 2 cm = 0.02 m, g = 9.8m/s 2. 323.4 354.2 600.2 323.4 938.5 631 569.4 631 600.2 446.4 452.6 446.4 631 600.2 815.5 WebA simple pendulum is defined to have an object that has a small mass, also known as the pendulum bob, which is suspended from a light wire or string, such as shown in Figure 16.13. WebSimple Pendulum Calculator is a free online tool that displays the time period of a given simple. Second method: Square the equation for the period of a simple pendulum. << /Linearized 1 /L 141310 /H [ 964 190 ] /O 22 /E 111737 /N 6 /T 140933 >> /Type/Font Resonance of sound wave problems and solutions, Simple harmonic motion problems and solutions, Electric current electric charge magnetic field magnetic force, Quantities of physics in the linear motion. (a) What is the amplitude, frequency, angular frequency, and period of this motion? Page Created: 7/11/2021. A simple pendulum is defined to have an object that has a small mass, also known as the pendulum bob, which is suspended from a light wire or string, such as shown in Figure 16.13. xYK WL+z^d7 =sPd3 X`H^Ea+y}WIeoY=]}~H,x0aQ@z0UX&ks0. It takes one second for it to go out (tick) and another second for it to come back (tock). An object is suspended from one end of a cord and then perform a simple harmonic motion with a frequency of 0.5 Hertz. 787 0 0 734.6 629.6 577.2 603.4 905.1 918.2 314.8 341.1 524.7 524.7 524.7 524.7 524.7 680.6 777.8 736.1 555.6 722.2 750 750 1027.8 750 750 611.1 277.8 500 277.8 500 277.8 xZYs~7Uj)?$e'VP$DJOtn/ *ew>>D/>\W/O0ttW1WtV\Uwizb va#]oD0n#a6pmzkm7hG[%S^7@[2)nG%,acV[c{z$tA%tpAi59t> @SHKJ1O(8_PfG[S2^$Y5Q }(G'TcWJn{ 0":4htmD3JaU?n,d]!u0"] oq$NmF~=s=Q3K'R1>Ve%w;_n"1uAtQjw8X?:(_6hP0Kes`@@TVy#Q$t~tOz2j$_WwOL. /LastChar 196 when the pendulum is again travelling in the same direction as the initial motion. 624.1 928.7 753.7 1090.7 896.3 935.2 818.5 935.2 883.3 675.9 870.4 896.3 896.3 1220.4 How long is the pendulum? Calculate gg. Study with Quizlet and memorize flashcards containing terms like Economics can be defined as the social science that explains the _____. 295.1 826.4 501.7 501.7 826.4 795.8 752.1 767.4 811.1 722.6 693.1 833.5 795.8 382.6 /Subtype/Type1 A grandfather clock needs to have a period of 460.7 580.4 896 722.6 1020.4 843.3 806.2 673.6 835.7 800.2 646.2 618.6 718.8 618.8 Compute g repeatedly, then compute some basic one-variable statistics. << 766.7 715.6 766.7 0 0 715.6 613.3 562.2 587.8 881.7 894.4 306.7 332.2 511.1 511.1 xA y?x%-Ai;R: 324.7 531.3 531.3 531.3 531.3 531.3 795.8 472.2 531.3 767.4 826.4 531.3 958.7 1076.8 384.3 611.1 675.9 351.8 384.3 643.5 351.8 1000 675.9 611.1 675.9 643.5 481.5 488 /Subtype/Type1 endobj That's a question that's best left to a professional statistician. 4 0 obj Perform a propagation of error calculation on the two variables: length () and period (T). /Type/Font (arrows pointing away from the point). Trading chart patters How to Trade the Double Bottom Chart Pattern Nixfx Capital Market. 4. >> 1999-2023, Rice University. This is for small angles only. Its easy to measure the period using the photogate timer. ollB;% !JA6Avls,/vqnpPw}o@g `FW[StFb s%EbOq#!!!h#']y\1FKW6 743.3 743.3 613.3 306.7 514.4 306.7 511.1 306.7 306.7 511.1 460 460 511.1 460 306.7 stream Problem (5): To the end of a 2-m cord, a 300-g weight is hung. /FontDescriptor 32 0 R /Widths[323.4 569.4 938.5 569.4 938.5 877 323.4 446.4 446.4 569.4 877 323.4 384.9 if(typeof ez_ad_units != 'undefined'){ez_ad_units.push([[300,250],'physexams_com-large-mobile-banner-2','ezslot_8',133,'0','0'])};__ez_fad_position('div-gpt-ad-physexams_com-large-mobile-banner-2-0'); Problem (10): A clock works with the mechanism of a pendulum accurately. << /FirstChar 33 The period is completely independent of other factors, such as mass. WebSo lets start with our Simple Pendulum problems for class 9. l(&+k:H uxu {fH@H1X("Esg/)uLsU. /Subtype/Type1 935.2 351.8 611.1] endobj The equation of period of the simple pendulum : T = period, g = acceleration due to gravity, l = length of cord. 285.5 799.4 485.3 485.3 799.4 770.7 727.9 742.3 785 699.4 670.8 806.5 770.7 371 528.1 /LastChar 196 WebSimple Pendulum Problems and Formula for High Schools. @ @y ss~P_4qu+a" ' 9y c&Ls34f?q3[G)> `zQGOxis4t&0tC: pO+UP=ebLYl*'zte[m04743C 3d@C8"P)Dp|Y What is the length of a simple pendulum oscillating on Earth with a period of 0.5 s? Solution: In 60 seconds it makes 40 oscillations In 1 sec it makes = 40/60 = 2/3 oscillation So frequency = 2/3 per second = 0.67 Hz Time period = 1/frequency = 3/2 = 1.5 seconds 64) The time period of a simple pendulum is 2 s. WebEnergy of the Pendulum The pendulum only has gravitational potential energy, as gravity is the only force that does any work. 0.5 1002.4 873.9 615.8 720 413.2 413.2 413.2 1062.5 1062.5 434 564.4 454.5 460.2 546.7 endobj Substitute known values into the new equation: If you are redistributing all or part of this book in a print format, /Name/F7 611.1 798.5 656.8 526.5 771.4 527.8 718.7 594.9 844.5 544.5 677.8 762 689.7 1200.9 /BaseFont/YQHBRF+CMR7 /FirstChar 33 WebAnalytic solution to the pendulum equation for a given initial conditions and Exact solution for the nonlinear pendulum (also here). Web1 Hamiltonian formalism for the double pendulum (10 points) Consider a double pendulum that consists of two massless rods of length l1 and l2 with masses m1 and m2 attached to their ends. << Hence, the length must be nine times. /FontDescriptor 17 0 R Figure 2: A simple pendulum attached to a support that is free to move. We see from Figure 16.13 that the net force on the bob is tangent to the arc and equals mgsinmgsin. WebFor periodic motion, frequency is the number of oscillations per unit time. Let's calculate the number of seconds in 30days. WebPeriod and Frequency of a Simple Pendulum: Class Work 27. endstream 495.7 376.2 612.3 619.8 639.2 522.3 467 610.1 544.1 607.2 471.5 576.4 631.6 659.7 351.8 935.2 578.7 578.7 935.2 896.3 850.9 870.4 915.7 818.5 786.1 941.7 896.3 442.6 1111.1 1511.1 1111.1 1511.1 1111.1 1511.1 1055.6 944.4 472.2 833.3 833.3 833.3 833.3 500 555.6 527.8 391.7 394.4 388.9 555.6 527.8 722.2 527.8 527.8 444.4 500 1000 500 The length of the cord of the first pendulum (l1) = 1, The length of cord of the second pendulum (l2) = 0.4 (l1) = 0.4 (1) = 0.4, Acceleration due to the gravity of the first pendulum (g1) = 1, Acceleration due to gravity of the second pendulum (g2) = 0.9 (1) = 0.9, Wanted: The comparison of the frequency of the first pendulum (f1) to the second pendulum (f2). stream Example 2 Figure 2 shows a simple pendulum consisting of a string of length r and a bob of mass m that is attached to a support of mass M. The support moves without friction on the horizontal plane. >> 571 285.5 314 542.4 285.5 856.5 571 513.9 571 542.4 402 405.4 399.7 571 542.4 742.3 Set up a graph of period vs. length and fit the data to a square root curve. endobj Look at the equation again. What is the answer supposed to be? We will then give the method proper justication. /Length 2854 The rope of the simple pendulum made from nylon. 6 0 obj /Type/Font 465 322.5 384 636.5 500 277.8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 [13.9 m/s2] 2. 323.4 877 538.7 538.7 877 843.3 798.6 815.5 860.1 767.9 737.1 883.9 843.3 412.7 583.3 /Name/F1 >> 0 0 0 0 0 0 0 0 0 0 0 0 675.9 937.5 875 787 750 879.6 812.5 875 812.5 875 0 0 812.5 Pendulum 1 has a bob with a mass of 10kg10kg. endobj x DO2(EZxIiTt |"r>^p-8y:>C&%QSSV]aq,GVmgt4A7tpJ8 C |2Z4dpGuK.DqCVpHMUN j)VP(!8#n The Results Fieldbook - Michael J. Schmoker 2001 Looks at educational practices that can make an immediate and profound dierence in student learning. We are asked to find gg given the period TT and the length LL of a pendulum. 4 0 obj citation tool such as, Authors: Paul Peter Urone, Roger Hinrichs. In trying to determine if we have a simple harmonic oscillator, we should note that for small angles (less than about 1515), sinsin(sinsin and differ by about 1% or less at smaller angles). 1. 384.3 611.1 611.1 611.1 611.1 611.1 896.3 546.3 611.1 870.4 935.2 611.1 1077.8 1207.4 Problem (1): In a simple pendulum, how much the length of it must be changed to triple its period? 513.9 770.7 456.8 513.9 742.3 799.4 513.9 927.8 1042 799.4 285.5 513.9] <> /Widths[622.5 466.3 591.4 828.1 517 362.8 654.2 1000 1000 1000 1000 277.8 277.8 500 What is the cause of the discrepancy between your answers to parts i and ii? We move it to a high altitude. WebSimple pendulum definition, a hypothetical apparatus consisting of a point mass suspended from a weightless, frictionless thread whose length is constant, the motion of the body about the string being periodic and, if the angle of deviation from the original equilibrium position is small, representing simple harmonic motion (distinguished from physical pendulum). 323.4 569.4 569.4 569.4 569.4 569.4 569.4 569.4 569.4 569.4 569.4 569.4 323.4 323.4 18 0 obj /Filter[/FlateDecode] are not subject to the Creative Commons license and may not be reproduced without the prior and express written /LastChar 196 298.4 878 600.2 484.7 503.1 446.4 451.2 468.8 361.1 572.5 484.7 715.9 571.5 490.3 20 0 obj 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 642.9 885.4 806.2 736.8 They recorded the length and the period for pendulums with ten convenient lengths. 295.1 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 295.1 x|TE?~fn6 @B&$& Xb"K`^@@ /Type/Font Describe how the motion of the pendula will differ if the bobs are both displaced by 1212. /Type/Font There are two constraints: it can oscillate in the (x,y) plane, and it is always at a xed distance from the suspension point. Solution: Recall that the time period of a clock pendulum, which is the time between successive ticks (one complete cycle), is proportional to the inverse of the square root of acceleration of gravity, $T\propto 1/\sqrt{g}$. Simple Harmonic Motion describes this oscillatory motion where the displacement, velocity and acceleration are sinusoidal. To compare the frequency of the two pendulums, we have \begin{align*} \frac{f_A}{f_B}&=\frac{\sqrt{\ell_B}}{\sqrt{\ell_A}}\\\\&=\frac{\sqrt{6}}{\sqrt{2}}\\\\&=\sqrt{3}\end{align*} Therefore, the frequency of pendulum $A$ is $\sqrt{3}$ times the frequency of pendulum $B$. are licensed under a, Introduction: The Nature of Science and Physics, Introduction to Science and the Realm of Physics, Physical Quantities, and Units, Accuracy, Precision, and Significant Figures, Introduction to One-Dimensional Kinematics, Motion Equations for Constant Acceleration in One Dimension, Problem-Solving Basics for One-Dimensional Kinematics, Graphical Analysis of One-Dimensional Motion, Introduction to Two-Dimensional Kinematics, Kinematics in Two Dimensions: An Introduction, Vector Addition and Subtraction: Graphical Methods, Vector Addition and Subtraction: Analytical Methods, Dynamics: Force and Newton's Laws of Motion, Introduction to Dynamics: Newtons Laws of Motion, Newtons Second Law of Motion: Concept of a System, Newtons Third Law of Motion: Symmetry in Forces, Normal, Tension, and Other Examples of Forces, Further Applications of Newtons Laws of Motion, Extended Topic: The Four Basic ForcesAn Introduction, Further Applications of Newton's Laws: Friction, Drag, and Elasticity, Introduction: Further Applications of Newtons Laws, Introduction to Uniform Circular Motion and Gravitation, Fictitious Forces and Non-inertial Frames: The Coriolis Force, Satellites and Keplers Laws: An Argument for Simplicity, Introduction to Work, Energy, and Energy Resources, Kinetic Energy and the Work-Energy Theorem, Introduction to Linear Momentum and Collisions, Collisions of Point Masses in Two Dimensions, Applications of Statics, Including Problem-Solving Strategies, Introduction to Rotational Motion and Angular Momentum, Dynamics of Rotational Motion: Rotational Inertia, Rotational Kinetic Energy: Work and Energy Revisited, Collisions of Extended Bodies in Two Dimensions, Gyroscopic Effects: Vector Aspects of Angular Momentum, Variation of Pressure with Depth in a Fluid, Gauge Pressure, Absolute Pressure, and Pressure Measurement, Cohesion and Adhesion in Liquids: Surface Tension and Capillary Action, Fluid Dynamics and Its Biological and Medical Applications, Introduction to Fluid Dynamics and Its Biological and Medical Applications, The Most General Applications of Bernoullis Equation, Viscosity and Laminar Flow; Poiseuilles Law, Molecular Transport Phenomena: Diffusion, Osmosis, and Related Processes, Temperature, Kinetic Theory, and the Gas Laws, Introduction to Temperature, Kinetic Theory, and the Gas Laws, Kinetic Theory: Atomic and Molecular Explanation of Pressure and Temperature, Introduction to Heat and Heat Transfer Methods, The First Law of Thermodynamics and Some Simple Processes, Introduction to the Second Law of Thermodynamics: Heat Engines and Their Efficiency, Carnots Perfect Heat Engine: The Second Law of Thermodynamics Restated, Applications of Thermodynamics: Heat Pumps and Refrigerators, Entropy and the Second Law of Thermodynamics: Disorder and the Unavailability of Energy, Statistical Interpretation of Entropy and the Second Law of Thermodynamics: The Underlying Explanation, Introduction to Oscillatory Motion and Waves, Hookes Law: Stress and Strain Revisited, Simple Harmonic Motion: A Special Periodic Motion, Energy and the Simple Harmonic Oscillator, Uniform Circular Motion and Simple Harmonic Motion, Speed of Sound, Frequency, and Wavelength, Sound Interference and Resonance: Standing Waves in Air Columns, Introduction to Electric Charge and Electric Field, Static Electricity and Charge: Conservation of Charge, Electric Field: Concept of a Field Revisited, Conductors and Electric Fields in Static Equilibrium, Introduction to Electric Potential and Electric Energy, Electric Potential Energy: Potential Difference, Electric Potential in a Uniform Electric Field, Electrical Potential Due to a Point Charge, Electric Current, Resistance, and Ohm's Law, Introduction to Electric Current, Resistance, and Ohm's Law, Ohms Law: Resistance and Simple Circuits, Alternating Current versus Direct Current, Introduction to Circuits and DC Instruments, DC Circuits Containing Resistors and Capacitors, Magnetic Field Strength: Force on a Moving Charge in a Magnetic Field, Force on a Moving Charge in a Magnetic Field: Examples and Applications, Magnetic Force on a Current-Carrying Conductor, Torque on a Current Loop: Motors and Meters, Magnetic Fields Produced by Currents: Amperes Law, Magnetic Force between Two Parallel Conductors, Electromagnetic Induction, AC Circuits, and Electrical Technologies, Introduction to Electromagnetic Induction, AC Circuits and Electrical Technologies, Faradays Law of Induction: Lenzs Law, Maxwells Equations: Electromagnetic Waves Predicted and Observed, Introduction to Vision and Optical Instruments, Limits of Resolution: The Rayleigh Criterion, *Extended Topic* Microscopy Enhanced by the Wave Characteristics of Light, Photon Energies and the Electromagnetic Spectrum, Probability: The Heisenberg Uncertainty Principle, Discovery of the Parts of the Atom: Electrons and Nuclei, Applications of Atomic Excitations and De-Excitations, The Wave Nature of Matter Causes Quantization, Patterns in Spectra Reveal More Quantization, Introduction to Radioactivity and Nuclear Physics, Introduction to Applications of Nuclear Physics, The Yukawa Particle and the Heisenberg Uncertainty Principle Revisited, Particles, Patterns, and Conservation Laws, A simple pendulum has a small-diameter bob and a string that has a very small mass but is strong enough not to stretch appreciably.
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