What is Pendulum: Definition and 1000 Discussions

A pendulum is a weight suspended from a pivot so that it can swing freely. When a pendulum is displaced sideways from its resting, equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back toward the equilibrium position. When released, the restoring force acting on the pendulum's mass causes it to oscillate about the equilibrium position, swinging back and forth. The time for one complete cycle, a left swing and a right swing, is called the period. The period depends on the length of the pendulum and also to a slight degree on the amplitude, the width of the pendulum's swing.
From the first scientific investigations of the pendulum around 1602 by Galileo Galilei, the regular motion of pendulums was used for timekeeping, and was the world's most accurate timekeeping technology until the 1930s. The pendulum clock invented by Christiaan Huygens in 1658 became the world's standard timekeeper, used in homes and offices for 270 years, and achieved accuracy of about one second per year before it was superseded as a time standard by the quartz clock in the 1930s. Pendulums are also used in scientific instruments such as accelerometers and seismometers. Historically they were used as gravimeters to measure the acceleration of gravity in geo-physical surveys, and even as a standard of length. The word "pendulum" is new Latin, from the Latin pendulus, meaning 'hanging'.

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  1. S

    Pendulum hitting a peg/conservation of energy

    Homework Statement A pendulum comprising a light string of length L and a small sphere swings in the vertical plane. the string hits a peg located a distance d below the point of suspension. (Diagram attached below). a) Show that if the sphere is released from a height below the peg, it...
  2. W

    Quality factor of driven damped oscillating pendulum

    Homework Statement A small cuckoo clock has a pendulum 25 cm long with a mass of 10 g and a period of 1 s. The clock is powered by a 200 g weight which falls 2 m between the daily windings. The amplitude of the swing is 0.2 rad. What is the Q (quality factor) of the clock? How long would the...
  3. W

    Quality factor of driven damped oscillating pendulum

    Homework Statement A small cuckoo clock has a pendulum 25 cm long with a mass of 10 g and a period of 1 s. The clock is powered by a 200 g weight which falls 2 m between the daily windings. The amplitude of the swing is 0.2 rad. What is the Q (quality factor) of the clock? How long would the...
  4. 1

    Oscillation vs. Pendulum Periods

    Homework Statement The rotational inertia of a uniform thin rod about its end is ML2/3, where M is the mass and L is the length. Such a rod is hung vertically from one end and set into small amplitude oscillation. If L = 1.0 m this rod will have the same period as a simple pendulum of...
  5. J

    Time period of a torsional pendulum

    For a piece of practical work, I'm investigating which factors alter the time period of a torsional pendulum. So far, I'm changing the mass of the pendulum, the length of wire, type of wire and thickness of wire, can anyone recommend anything else? Also, I'm looking at the formula...
  6. QuarkCharmer

    Ballistic Pendulum kinetic energy

    Homework Statement A 11.0 g rifle bullet is fired with a speed of 360 m/s into a ballistic pendulum with mass 9.00 kg, suspended from a cord 70.0 cm long. A.) Compute the initial kinetic energy of the bullet B.) Compute the kinetic energy of the bullet and pendulum immediately after the...
  7. P

    Pendulum in a Car: Solving Homework Statement

    Homework Statement A pendulum of mass 1.0 kg is suspended from the roof of a car traveling on a level road. An observer in the car notices that the pendulum string makes an angle of 10 deg with the vertical. What is the acceleration of the car? Homework Equations Fc=mv^2/r The...
  8. F

    Period of a pendulum is measured to be 3.00 s

    Homework Statement The period of a pendulum is measured to be 3.00 s in the reference frame of the pendulum. Homework Equations What is the period when measured by an observer moving at a speed of 0.960c relative to the pendulum? The Attempt at a Solution I don't want to...
  9. B

    How to Calculate g with Known Pendulum Length and Negligible Amplitude?

    How to calculate g if amplitude of a simple pendulum is negligible and the length is known? T=2π\sqrt{}l/g
  10. S

    Pendulum on Pendulum, velocity in non inertial frame

    Homework Statement A double pendulum consists of two particles of equal mass m suspended by massless rods of equal length l. Assuming that all motion is in a vertical plane: 1. Find the Lagrangian of this system. 2. then find the equations of motion and, 3. linearize these equations...
  11. M

    Calculating Pendulum Drop Distance for 45 Degree Angle - Homework Help

    Homework Statement i need to calculate the d for a 45 degree drop of pendulum that the length is .44m. i did the one for 90 degrees but i can't figure out how to get a different outcome. Homework Equations ug initial= KE + Ug final mgh=0.5mv^2=mgh gl=0.5rg+g2r l=0.5r+2r...
  12. P

    Calculating Energy Loss with Ballistic Pendulum

    Homework Statement How was energy lost while using the ballistic pendulum? Homework Equations Initial KE= 1/2mb*Vb^2 = 0.929J Final Potential graviational = (m+M)gh= 0.198J Energy loss = 0.929J - 0.198J= 0.731J The Attempt at a Solution I think the answer is: energy lost dues to...
  13. J

    What is the radial acceleration of a pendulum at a given angle?

    A pendulum (with string length "L") and aball of mass "m" is pulled back to a horizontal position and then released. Assuming that θ is the angle between the string and the vertical, find (a.) the magnitude of the radial acceleration of this ball at an angle of θ as a function of m,g, L, and/or...
  14. J

    Pendulum Problem with unknown angle

    A pendulum (with string length "L") and aball of mass "m" is pulled back to a horizontal position and then released. Assuming that θ is the angle between the string and the vertical, find the speed of the ball (v) at an angle of θ as a function of m,g,L, and/or θ. I just can't get my...
  15. L

    Does mass affect the period of a pendulum attached to an elastic string?

    if if we have a string and a object with mass m connected to it , it does extend for 11 cm (string) . if we put another object with the same mass m , what will be the period of that ( of the 2 objects in the string) . please explain does mass affect the period ? thnx
  16. S

    Pendulum Problem: Potential energy equals? kinetic energy

    Homework Statement A pendulum consists of an object of mass m = 1.65 kg swinging on a massless string of length l. The object has a speed of 1.97 m/s when it passes through its lowest point. If the speed of the object is 0.87 m/s when the string is at 70° below the horizontal, what is the...
  17. P

    Elastic Collision w/ Pendulum Bobs

    1. A pendulum bob of mass m is released from a height H above the lowest point. It collides at the lowest point with another pendulum of the same length but with a bob of mass 2m initially at rest. Find the heights to which the bobs rise given that the collision is (A) Completely Inelastic...
  18. A

    Physical pendulum made of a uniform disk

    Homework Statement A physical pendulum is made of a uniform disk of mass M and radius R suspended from a rod of negligible mass. The distance from the pivot to the center of the disk is l. What value of l makes the period a minimum? Homework Equations The Attempt at a Solution
  19. D

    Horizontal Force to Hold Pendulum Perpendicular

    Friends: Recently I got this problem: what sustained horizontal wind pressure/force is needed to make a pendulum swing up and stay at a certain angle? To solve this problem, I imagined applying a horizontal force FH to the bob (of mass "m"). I learned that the angle that the pendulum makes...
  20. W

    Exploring the Mechanics of a Pendulum's Swing

    Homework Statement When I release a large pendulum from about my eye level, why does it not return and hit my face? Homework Equations PE=mgh and KE= 1/2mv^2 possibly? The Attempt at a Solution I was thinking that it had something to do with a transfer of potential energy to...
  21. Low-Q

    Pendulum with a Spring: Analyzing Damping Effects

    Hi, I just wonder what happens if a pendulum is attached to a pivot point via a flexible spring, and the spring is: 1 Not damped 2 Partially damped Will the pendulum stop earlier, or will it sustain as long as a pendulum with no spring attached to it? Vidar
  22. K

    Rifle Bullet Pendulum (Solved just on 1 aspect)

    Homework Statement A 36 g rifle bullet traveling 310 m/s buries itself in a 5.2 kg pendulum hanging on a 2m long string, which makes the pendulum swing upward in an arc. Determine the maximum verticle displacement of the pendulum (height)(g=9.8m/s^2) Homework Equations Pi = Pf Law of...
  23. J

    Quantum Pendulum: Solving in Heisenberg Interp.

    Hy I am trying to solve problem of quantum pendulum in region of unstable equilibrium. I am doing it in Heiseberg interpretation of QM. The equation of motion that I am getting is \dot{\dot{\theta}} = \omega^2\theta , and the solution is in form of : x (t) = A\cosh(\omega t) + B\sinh...
  24. G

    Is the velocity of a pendulum at the height of its swing 0?

    I would think that at a pendulum's highest point the velocity would be 0. Am I wrong in my assumption?
  25. G

    How do you calculate the velocity of a pendulum at its lowest point?

    If you are given the tension of the pendulum at its lowest point and the length of the pendulum, how can you solve for the velocity of the pendulum? I've looked in my book and found the equation v= √ (2gL (1-cosΘ)) But this equation doesn't help me unless I have the maximum angle the...
  26. A

    Deriving the Equation for Period of Simple Pendulum? Is my attempt correct?

    Homework Statement I have to derive an equation with the following variables: T= period m= mass Theta= angle l= length and I was told to think of the period as the perimeter of a circle.Homework Equations The Attempt at a Solution C=2\pi r,C/2=\pi r,d=\pi r,(at^2)/2=\pi r,t=\sqrt{\frac{2\pi...
  27. I

    Pendulum Motion Equation and Period Calculation

    Hi guys, I was doing my lab report and stumbled onto this question and I would really appreciate it if you guys could assist me on this. (: Homework Statement For a simple pendulum consisting of a mass M attached to a very thin light string of length L, in the absence of air resistance...
  28. C

    Comp Sci Spring pendulum system fortran program

    I just want to know if someone has the fortran code for the numerical solution of the pendulum with a spring. And if it is so, can it write it here?
  29. C

    Simple harmonic oscillators and a pendulum clock.

    Hey physics forums, this is my first post and frankly I'm having trouble conceptualizing this problem. I know harmonic oscillation is involved, as it is a pendulum. However, I know I have to incorporate g into the s.h.o. equation and I'm not quite sure how to do that. Any help would be...
  30. B

    Frequency of a simple pendulum

    A simple pendulum of length L and mass m is suspended in a car that is traveling with constant speed v around a circle of radius R. If the pendulum undergoes small oscillations in a radial direction about its equilibrium position, what will its frequency of oscillation be? I don’t know how to...
  31. A

    Uncertainty with a simple pendulum

    A simple pendulum is used to measure the acceleration of gravity using T=2pi(sqrt(L/g)) . The period T was measured to be 1.24 ± 0.02 s and the length L to be 0.381 ± 0.002 m. What is the resulting value for g with its absolute and relative uncertainty? So the first thing I did was to isolate...
  32. H

    Pendulum (Conservative Forces and Potential Energy

    Homework Statement A mass m = 6.3 kg hangs on the end of a massless rope L = 2.13 m long. The pendulum is held horizontal and released from rest. I already found the speed at the bottom of the pendulum's path and that is 6.46. I'm stuck on: a. What is the magnitude of the tension...
  33. S

    Direction of acceleration in pendulum bob?

    A simple pendulum consists of a mass M tied to a string and swings freely starting from rest at the position on the left in the figure below. http://imageshack.us/photo/my-images/695/screenshot20110922at611.png/ Select the vectors which best represent the acceleration of mass M at the...
  34. M

    Acceleration of a compound pendulum

    Homework Statement A uniform thin rod of mass M and length L is supported horizontally by two supports, one at each end. The acceleration of gravity, g, is constant and in the downward direction. At time t=0 the left support is removed. Find the downward acceleration of the center of mass at...
  35. C

    How to Optimize Mass and Attachment in a Spring Pendulum Experiment?

    Homework Statement Hey guys I need help with a spring pendulum experiment. The practical part of the project is designing it, and gathering at least one set of measured data - independent/dependent variables. The system will exhibit both motions of a simple pendulum AND a simple spring system...
  36. J

    SHM Pendulum length/gravity question

    T= 2pie Square root of 2L/3g I got a couple of questions. 1) why is it 2L/3g? 2) would my straight line graph be T^2 vs L? ( so gradient is T^2/l?) 3) after i get my gradient do i compare it to the gravity 9.81? 4) is the equation going to be time^2=XXL or s^2=xxm ? do i use the unit...
  37. J

    Pendulum with time dependent length

    Homework Statement A mass m is suspended by a massless string of varying length l = l0 - vt, where v is constant. The mass is released at angle [\theta]0 from rest. (a) Write down the Lagrangian and find the equation of motion (b) Show that these equations reduce to those of a simple...
  38. J

    Two Masses on Same String - Conical Pendulum

    3.(a) A particle P, of mass 0.03kg, is attached to one end of a light inextensible string OP, of length 1 m. The other end of the string is attached to a fixed point O. The particle moves in a horizontal circle, with centre vertically below O, at an angular speed of 2 revolutions per second. The...
  39. C

    Question on the equation for the period of a pendulum

    [a]1. Homework Statement [/b] essentially my "problem statement" is to determine what the mg in the equation T=2π√(I/mgL) is being used to represent Homework Equations T=2π√(I/mgL) The Attempt at a Solution in a nutshell, i solved a difficult problem in a way that my...
  40. N

    Equation of motion for pendulum with slender rod (energy method)

    hey guys, I have a question regarding how to get the potential energy for this. I can get the correct answer, but the solutions do a step that makes absolutely no sense to me, so hopefully someone leads me in the right direction :smile: Homework Statement Using energy method, derive the...
  41. C

    Calculate Fraction to Change Length of Pendulum for True Run

    Homework Statement by what fraction must you change the length of the pendulum to make it run true if it loses one minute every hour Homework Equations t=2pi/sqrt(g) * sqrt(l) The Attempt at a Solution I know that I am losing 1 second every 60 seconds so I need to shorten the period...
  42. K

    Conservation of energy of a pendulum

    A pendulum is suspended from the ceiling and attached to a spring fixed to the floor directly below the pendulum support. The mass of the pendulum bob is m, the length of the pendulum is L, and the force constant is k. The unstressed length of the spring is L/2 and the distance between the...
  43. P

    Critical Angle of an Inverted pendulum

    Hi everyone, I’m designing and building an inverted pendulum on a cart for a 3rd year undergrad engineering course. So far i have been going quite well, but i have come across a question and it has me completely stumped. Any help would be great Homework Statement The pendulum on a cart only...
  44. L

    A falling pendulum question

    Homework Statement Hi, this is supposed to be an easy question, but for some reason I can't get it to work. The question is: A weightless rod is hinged at O so that it can rotate without friction in a vertical plane. A mass m is attached to the end of the rod A, which is balanced...
  45. B

    Solving Parallel Plate Capacitor Pendulum Oscillations

    1. Homework Statement PLEASE DO NOT DELETE THIS POST, MODS, IT MAY LOOK LIKE THE SAME QUESTION AS BEFORE, BUT IT IS NOT, IT IS A TOTALLY DIFFERENT PART TO THE QUESTION. consider a parallel=plate capacitor with square plates of side L and distance d (<<L) between them, charged with charges...
  46. K

    Conservation of Energy of a pendulum

    A pendulum consists of a 2.0-kg bob attached to a light 3.0-m-long string. While hanging at rest with the string vertical, the bob is struck a sharp horizontal blow, giving it a horizontal velocity of 4.5 m/s. At the instant the string makes an angle of 30° with the vertical, what is (a) the...
  47. S

    Polynomial expression of Pendulum period with respect to angle (large)

    [b]1. Homework Statement The swinging period T(θ) for a small amplitude simple pendulum, is given by T, a constant for a constant length pendulum. If the initial angle θ is large, then the amplitude becomes large and the period needs to be corrected. The correction to the large amplitude...
  48. S

    What Would Happen to a Newton's Pendulum in Space?

    I was wondering what will happen if we had a Newton's pendulum (cradle ) in space out of any significant gravitational orbit, although one with only two balls where the string attached to each balls would only be tied to the same center. This pendulum would allow the first ball to hit the...
  49. B

    Consider a pendulum of length d/2 calculate the electric field inside capacitor

    Homework Statement consider a parallel-plate capacitor with square plates of side L and distance d (<<L) between them, charged with charges +Q and -Q. The plates of the capacitor are horizontal, with the lowest lying on the x-y plane, and the orientation is such that their sides are...
  50. T

    Double Pendulum Motion: Plotting theta2 vs Time

    Hello all, I have written a python code implementing the Runge-Kutta fourth order method for higher orders to approximate the motion of a double pendulum. The problem I am having is that my plot of theta2 (angle of second rod) Vs time looks a little off and I am curious if I have it correct...
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