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timekeeper, used in homes and offices for 270 years, and achieved accuracy of about one second per year before it was superseded as a time standard by the quartz clock in the 1930s.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'.

View More On Wikipedia.org
  1. C

    Conserved quantities in the cart and pendulum problem

    A problem on an assignment I'm doing deals with a cart of mass m1 which can slide frictionlessly along the x-axis. Suspended from the cart by a string of length l is a mass m2, which is constrained to move in the x-y plane. The angle between the pendulum and vertical is notated as phi. The...
  2. P

    Partial derivative of a square root

    Hi, I'm using partial derivatives to calculate propagation of error. However, a bit rusty on my calculus. I'm trying to figure out the partial derivative with respect to L of the equation: 2pi*sqrt(L/g) (Yep, period of a pendulum). "g" is assumed to have no error. I know I can use the...
  3. F

    Equations of motion for a fixed-height inverted pendulum

    Hi everybody! I'm struggling with a physics problem I though I had solved, but as it is turning out recently, I probably hadn't. The problem might actually be pretty easy, just me being unable to solve properly. All of you are familiar with inverted pendulum. Now, imagine an inverted pendulum...
  4. P

    Period and Tension of a Pendulum

    Homework Statement A simple pendulum experiment is constructed from a point mass m attached to a pivot by a massless rod of length L in a constant gravitational field. The rod is released from an angle θ0 < π/2 at rest and the period of motion is found to be T0. Ignore air resistance and...
  5. O

    How Do You Measure the Length of a Pendulum with Non-Spherical Bobs?

    Hello, I should preface that we are not physicists. We are just a few relatively ordinary guys that committed to building a large pendulum wave (6ft tall, 8ft long). The construction went very well. The frame and the individual pendulum are all strung up. We have a rather ingenious rig that...
  6. H

    K.E. and P.E. in a Pendulum and Spring

    Can anyone explain the conversion of K.E and P.E during compression and expansion of spring and during the motion of pendulum ?
  7. terryds

    A Curious question About Ballistic Pendulum Solution

    I've watched a video about ballistic pendulum problems. The illustration is : I wonder why the final energy is just a gravity potential energy. I think there is also a rotational kinetic energy (since it will rotate and oscillate) Is my thought wrong?
  8. U

    Pendulum - Stability and fixed points

    Homework Statement (a): Show the lagrangian derivative in phase space (b)i: Show how the phase space evolves over time and how they converge (b)ii: Find the fixed points and stability and sketch phase diagram (c)i: Find fixed points and stability (c)ii: Show stable limit cycles exist for T>ga...
  9. Satvik Pandey

    Angular Momentum of a conical pendulum.

    Homework Statement A small ball of mass m suspended from a ceiling at a point O by a thread of length l moves along a horizontal circle with constant angular velocity ##\omega##. Find the magnitude of increment of the vector of the ball's angular momentum relative to point O picked up during...
  10. K

    How to calculate external force acting on a pendulum

    I am doing a physics project whose purpose involves describing the physics behind a toy. The toy I have selected is a "decision maker" which is composed of a pendulum which has a magnetically charged ball on it that swings side to side, while having a force exerted on it by magnets which change...
  11. M

    How Does Torque Balance Apply to an Upside Down Vertical Pendulum?

    hi pf! i am looking at a simply problem dealing with an upside down vertical pendulum of length ##L## having mass ##m## at the top. i believe my professor wrote that a torque balance yields ##m \ddot{\theta} = mg\sin \theta + f(t)## where ##f## is a torque (i think) and ##\theta## is the angle...
  12. J

    Vertical energy of a pendulum - is there one?

    Homework Statement Hello. I was just wondering. You have a simple pendulum . string and a ball with mass at the end. We usually solve examples and we think about conversation of kinetic energy and potentional energy. I was just wandering if there is also something like vertical kinetic energy...
  13. S

    Divide by Zero Error: Solving Pendulum Radius

    I have data from a pendulum and I am using it to work out the radius of the pendulum. I have acceleration in the x and y directions and so thought this would be easy enough. Simply I determine the (velocity in the x direction)^2/acceleration in the y direction. However when I use python to give...
  14. DaTario

    Are Pendulum Waves Truly Waves Without Physical Connections?

    Hi All, I use to teach wave theory and I like to discuss the example of pendulum waves, which is easy to find at internet, for instance, ). My question has to do with stating that this pendulum waves are not waves, for there is no physical connection between the oscillators...
  15. oreo

    Pendulum measuring acceleration of car

    I came across this problem which says" A pendulum is hung by roof of a train having mass 1 kg . The train then accelerates and pendulum makes an angle with vertical. What is acceleration of train? " Is it equal to gsinθ?
  16. A

    Double pendulum - solving with energy and Simulink

    Hi everyone, I am trying to familiarize myself with Simulink by graphically drawing out differential equations, but ran into a snag with a double pendulum on a cart. Anyways, I neglect friction or other damping effects and say that From there I simply just sum the energies, which ends up...
  17. ubergewehr273

    How Does a Pendulum Bob's Speed Relate to Its Displacement Angle?

    Homework Statement Show that a simple pendulum bob which has been pulled aside from its equilibrium position through an angle ##\theta## and then released will pass through the equilibrium position with speed ##v = \sqrt{2gl(1-cos\theta)}##, where ##l## is the length of the pendulum. Homework...
  18. A

    Possible sources of error/uncertainty in bifilar pendulum?

    in my AH physics investigation - measuring acceleration due to gravity, I used the bifilar suspension pendulum btw a light gate was used for the errors/problems section so far I have problems in making the rod level and keeping the two strings parallel, also all the random, calibration and...
  19. A

    Possible sources of error in compound pendulum experiment?

    completing my advanced higher physics investigation - measuring acceleration due to gravity for the oscillating mass on a spring experiment so far I have included friction between the nail & oscillating rod as a possible source of error can anyone think of anything else? thank you very much...
  20. R

    MHB Help with motions of a double pendulum using RK4

    Hello everyone, :)I hope you consider this the right place for this question. I have been working way to long on making a model of a double pendulum using the RK4 method with excel. I have these four equations that I should be able plug into RK4 I know that the first two equations for...
  21. K

    Pendulum Oscillations: 24/min, 1.53m Long, Find Gravity

    Homework Statement A pendulum oscillates 24.0 times per minute in a particular location. If the pendulum is 1.53 m long, what is the acceleration due to gravity there? Homework Equations T = 2π√ l/g The Attempt at a Solution I don't have one because i literally got into this unit. I am...
  22. Vanessa Avila

    Calculating the Speed of a Pendulum Bob Using Energy Equations

    1.) Homework Statement A(n) 2.71 m long pendulum is released from rest when the support string is at an angle of 35.8◦ with the vertical. The acceleration of gravity is 9.8 m/s2 . What is the speed of the bob at the bottom of the swing? Answer in units of m/s 2.) Relevant equations Not sure...
  23. D

    Pendulum and spinning mass -- Coupled

    Homework Statement Imagine two masses connected to each other by a string. One mass sits atop a table, while the other mass dangles below the table, as the string is fed through a hole in the center. The configuration looks like this...
  24. W

    Pendulum Equilibrium: Can It Pass Balance Point Twice?

    Consider a pendulum in it's balance point hanging from ceiling. It can swing in all the directions in the space. The pendulum can only swing in a sphere(the string can't bend). Now, is it possible to release the pendulum in a particular height and with a initial condition that in the first...
  25. Z

    Time to Reach Highest Speed of Simple Pendulum

    Homework Statement You pull a simple pendulum of length 0.260m to the side through an angle of 3.50∘ and release it. Part A: How much time does it take the pendulum bob to reach its highest speed? Part B: How much time does it take if the pendulum is released at an angle of 1.75∘ instead of...
  26. S

    Radial acceleration in a pendulum

    I'm just trying to think how I would expect radial acceleration to look like in a pendulum. I would expect a sine wave of sorts but instead of oscillating around zero I would expect it to be around a positive number as this acceleration is always in the same direction. Also if I was to compare...
  27. W

    Pendulum with a bob that changes its center of mass

    Hello all, this is my first post here. I will try to phrase it as best I can, my physics background is weak, so please be patient, and thanks in advance for your help! I tried researching simple pendulums but couldn't quite find an answer. Suppose a person is suspended, prone, from a pendulum...
  28. J

    How to find the amplitude of a pendulum

    How do I find the amplitude of a pendulum with the given information: Length=0.5 m Mass=0.25 kg x=0.2 m k (constant)=12.25 N/m Thanks!
  29. stripes

    Model Quadruple Pendulum in Mathematica: Interesting Questions & Patterns

    I've successfully modeled a quadruple linked pendulum in Mathematica. I've done a few interesting things with the simulation. I've shown angles vs. time, and how a tiny change in initial conditions result in a completely different, unpredictable path for the masses of the pendulum. I've shown...
  30. A

    Simple Pendulum Project: Amplitude's Effect on Period | Math Help Included

    nee help with project dealing with simple pendulum.I am supposed to be looking at the effect of changing the amplitude and how it affects the period. The requirements want to show some math( it does not include finding average and error). Need help. what could I show there. Like the time to...
  31. S

    Inverted Pendulum Dynamics Identification

    Homework Statement I am trying to establish the the dynamics of an inverted pendulum for further analysis. I understand that this is a well known problem, but the governing equations in various sources are different and make it difficult to keep track of what forces are being applied on the...
  32. S

    How Does Measuring Position Impact Speed Measurement Accuracy in a Pendulum?

    Homework Statement We have a pendulum in thermal balance with the surroundings - no damping. We measure the speed of the pendulum. The accuracy of each speed measurement is known. How does the accuracy of the speed change, if we decide also measure the position of the pendulum with accuracy 10%...
  33. B

    Dimensional analysis of a physical pendulum

    Hi! Sorry if this is the wrong section to post this: I am doing a laboration on physical pendulums and I have a bit of trouble making sense of it all and I am in need of some guidance. When I do the analysis I get the standard mathematical pendulum. [T]=[m]^a*[l]^b*[g]^c, where a = 0, b = -c...
  34. S

    Lagrange mechanics: Pendulum attached to a massless support

    Homework Statement A simple pendulum of length ##b## and bob with mass ##m## is attached to a massless support moving vertically upward with constant acceleration ##a##. Determine (a) the equations of motion and (b) the period for small oscillations. 2. Formulas ##U = mgh## ##T = (1/2)mv^2...
  35. H

    Pendulum problem: particularly the wording Rest position.

    The Attempt at a Solution It seems as though the rest point is at the ends of the pendulum swing. I know that the period of a pendulum is the time it takes the pendulum to make one full back-and-forth swing. I think this problem is wrong if the rest point means equilibrium point. Because then...
  36. L

    Conservation of Energy Problem -- bullet fired into a ballistic pendulum

    Homework Statement A bullet has a mass of 7.5 g. It is fired into a ballistic pendulum. The pendulum's receiving block of wood is 2.5 kg. After the collision, the pendulum swings to a height of 0.1 m. What is the approximate velocity of the bullet? m_{bullet} = 7.5g = 0.0075 kg m_{wood} = 2.5...
  37. J

    Help with coupled spring and pendulum system

    Homework Statement Given the system in the image below, I need to find the equation of motions for the coupled system. The surface where the block moves is frictionless. The red line is position where the block is at equilibrium. At equilbrium x1 and x2 = 0. After finding the equation of motion...
  38. D

    Pendulum Oscillation Frequency?

    Homework Statement Given a pendulum with fixed length, at what angle does the pendulum have to be released at in order to not follow the standard formula for frequency? Homework Equations P = 2pi*sqrt(l/g) The Attempt at a Solution I know that this equation holds for "small" angles (theta <...
  39. O

    An issue with Conical Pendulums

    Homework Statement A conical pendulum with an unelastic tether has a mass of 4.25 kg attached to it. The tether is 2.78 m. The mass travels around the center every 3.22 seconds. What angle does the rope make in relation to its original position? m=4.25 kg T=3.22 s L=2.78 m Homework Equations...
  40. M

    Calculating Pendulum Angle and Amplitude: Homework Question and Equations

    Homework Statement a)The angle that the string of a long pendulum makes with the vertical is shown as a function of time. What is the angular frequency of the pendulum? b)What is the amplitude of the pendulum's motion, in meters? Homework Equations Angular frequency=sqrt(g/L)The Attempt at a...
  41. ORF

    In QM, can the trajectory in the phase-space split?

    Hello. I was told that "in QM the information doesn't disappear". Does it mean that, in QM, the trajectory in the phase-space can't split? [The typical example is a vertical simple pendulum, with the mass above the spin-point; in classical mechanics you can't know if the pendulum will fall one...
  42. grandpa2390

    How do I set up this pendulum problem with a pivot point not on edge

    Homework Statement Damped driven oscillator: ruler example. Suppose the ruler used in the classroom demonstration has a length of 12 and 13/16ths inches, a width of 1 ½ inches, is 1/16th inch thick with a density of 1.2 g/cm3. It swings from a pivot point ¼ of an inch from the top end. a) Find...
  43. B

    Simple Harmonic Motion Pendulum problem

    Homework Statement A simple pendulum of length =30.0cm is released from rest from an angle of θ=10.0∘ to the vertical. Assuming that the pendulum undergoes simple harmonic motion, find its maximum speed. Source: https://isaacphysics.org/questions/accuracy_shm_pendulum_num Homework Equations a)...
  44. J

    Quantum Pendulum: Probability of Ground State After Length Change

    Homework Statement A particle is in the ground state of a pendulum of length ##L##. ##L## suddenly increases to ##4L##. Find the probability that the particle will be in the ground state of the new pendulum. Homework EquationsThe Attempt at a Solution What's this question even asking? So the...
  45. N

    Simple pendulum equation of motion

    Hi! I've been trying to find the equation of motion for the simple pendulum using x as the generalized coordinate (instead of the angle), but I haven't been able to get the right solution... Homework Statement The data is as usual, mass m, length l and gravity g. The X,Y axes origin can be...
  46. DavitosanX

    Homogeneous 2nd Order DE from spring pendulum

    I'm currently taking a Classical Mechanics course, and we're studying the lagrangian equation. After a few exercises, I thought I'd try to come up with the motion equations for a pendulum where the mass hangs from a spring. The resulting differential equations take a form that I don't really...
  47. T

    Simple Pendulum: The gradient of the graph of T^2 against length

    I've been asked to investigate the value of g. My graph shows that the gradient is around 4.4 as when the length was 0.27m, the squared time period was 1.18s (since this is a T2 against L graph). My question is, of course, why? If I am detecting g, which is 9.81 on earth, why did I get such...
  48. T

    Calculating the Period of a Simple Pendulum

    A simple pendulum is suspended from a ceiling 3.2m high and the bob height from the floor is measured to be 68cm. Calculate the period of small amplitude oscillations of the bob. I converted 68cm to 0.68m. The total length of the pendulum must be 3.2 - 0.68 = 2.52. When working with the...
  49. Yae Miteo

    Pendulum Velocity Homework: Find Mass's Speed at Bottom of Path

    Homework Statement A mass m = 5.5 kg hangs on the end of a massless rope L = 1.81 m long. The pendulum is held horizontal and released from rest. How fast is the mass moving at the bottom of its path? Homework Equations a_c = \frac {v^2}{r} F = ma v = v_o + at The Attempt at a Solution I...
  50. T

    Simple Pendulum Damping: Finding Amplitude and Energy Loss Rate

    Homework Statement Consider a simple pendulum (point mass bob) 0.55m long with a Q of 370. a) How long does it take for the amplitude (assumed small) to decrease by two-thirds? b) If the amplitude is 2.9cm and the bob has mass 0.22kg , what is the initial energy loss rate of the pendulum...
Back
Top