Pendulum Definition and 1000 Threads

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timekeeper, used in homes and offices for 270 years, and achieved accuracy of about one second per year before it was superseded as a time standard by the quartz clock in the 1930s.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

    Elastic Spring / Simple Pendulum Lowest Point

    Homework Statement A perfectly elastic spring swings in a vertical plane as a simple pendulum with a mass m suspended at the bottom of the spring. The force constant for this spring is ##k## and the unstretched length is ##L##. The spring is carefully held in the horizontal position so that the...
  2. J

    Experiment to determine the time period of a pendulum

    Homework Statement Homework EquationsThe Attempt at a Solution Time period of a simple pendulum is given by 2π√(L/g) . By uniform mass distribution , I am assuming density of mass of bob to be constant . I don't understand how time period depends on the mass of the bob of a simple pendulum .
  3. P

    Finding the period of a pendulum witha string that has mass

    1. The problem statement, all variables and gihttps://www.physicsforums.com/attachments/218400 ven/known data Assuming the string from a simple pendulum did not have negligible mass and the pendulum bob was not a point mass, then determine an expression for the period of a single small-amplitude...
  4. B

    Gravitational potential energy of a coupled pendulum

    Homework Statement I'm trying to solve problem a problem of complete energy of doubled pendulum (2 mathematical pendulums connected by a string). For a kinetic energy I would get (1/2) J(w_1)ˆ2 + (1/2) J(w_2)ˆ2 and for a potential energy of a spring (1/2) k (ϕ_1-ϕ_1) What about gravitational...
  5. A

    Quick Question about Pendulum Graphs

    Hi everyone. I just have a very quick question regarding position time graphs and velocity time graphs for a pendulum. As we know, at the maximum displacement, the acceleration is at its maximum and the velocity is zero, and vice versa when the displacement is zero. When we put this...
  6. Pushoam

    Approximation for a slipped pendulum

    Homework Statement Homework EquationsThe Attempt at a Solution Applying conservation of potential energy, ## mgL (1 - \cos{ \theta_0}) = mg(L + \delta ) (1 - \cos{ \theta_1}) ## ## \cos{ \theta_1} - \cos{ \theta_0} = \frac { \delta - \delta \cos{ \theta_1}} L ##Taking the...
  7. V

    Gravitational Effects on a Pendulum in a Moving Ship

    Homework Statement A pendulum having a bob of mass ##m## is hanging in a ship sailing along the equator from east to west. If the ship sails at speed v what is the tension in the string?. Angular speed of Earth's rotation is ## \omega ## and radius of the Earth is ## R ## Homework Equations...
  8. G

    Does a Pendulum Stop Swinging in a Falling Lift?

    Assume a pendulum was swinging in a lift. If the cable breaks and the lift starts to accelerate down at g would the pendulum stop swinging and freeze in its current position? Merry Xmas. G.
  9. C

    The length of a pendulum that is equivalent to a rocking hemisphere

    Homework Statement A solid sphere is cut in half and a homogeneous hemisphere of radius r and mass M is set upon a table(with its flat side up). The surface of the table is perfectly rough. The hemisphere rocks back and forth with small amplitude excursions from equilibrium. What is the length...
  10. Pushoam

    Average tension force acting on a simple pendulum

    Homework Statement Homework EquationsThe Attempt at a Solution Trying to answer it before solving it, The maximum tension force is mg, so the average has to be less than this. Hence, the option (a) and (c) are not correct. ## T = mg \cos \theta ##, where ## \theta ## is the angle between...
  11. AbigailG

    Find an Expression for the Frequency - Pendulum

    Homework Statement [/B] A solid sphere of mass M and radius R is suspended from a thin rod. The sphere can swing back and forth at the bottom of the rod. Find an expression for the frequency of small angle oscillations.Homework Equations f = 1/2(pi) sqrt(MgR/I) I for a solid sphere 2/5MR^2The...
  12. xaratustra

    Foucault pendulum and a round globe

    Imagine we are all cavemen without satellite technology and just discovered the Foucault pendulum! As we know the angle of presession depends on the latitude. This can be used to prove that the Earth is rotating, right? Now by putting several Foucault pendula around the Earth, at equidistant...
  13. W

    Lagrangian: Pendulum down a slope

    Homework Statement I have the answer for part a, which is: $$\theta '' + \frac{a}{r} \cos \theta + \frac{g}{r} \sin \theta$$ My issue lies with getting the following equation of motion for part b, $$\theta '' + \frac{g}{r} \cos \alpha \sin \theta = 0$$ Homework EquationsThe Attempt at a...
  14. H

    Lab: Conical Pendulum - Understanding A & Unit

    So I'm doing a lab in class, and when I graphed the Period vs Length of the string, I got it in the form $T=A\sqrt{L}$, but I don't really know what the value $A$ represents nor what its unit is... Can someone help me?
  15. M

    MHB Double pendulum: energy function

    Hey! :o I am looking at the following: Find the energy function for the double pendulum, with vertical constant and uniform gravity field for motion restricted at vertical plane for motion in space We have that the energy function is the sum of the potential and the kinetic energy...
  16. Alexanddros81

    Simple Pendulum motion - Numerical Integration

    Homework Statement The differential equation of motion for the simple pendulum can be shown to be ##\ddot {θ} = -(g/L)sinθ##. Given that L=9.81 m and that the pendulum is released from rest at θ=60deg, determine the time required for the pendulum to reach the position θ=0deg. Use Δt=0.10s, and...
  17. Clara Chung

    Classical mechanics question (pendulum)

    Homework Statement Homework EquationsThe Attempt at a Solution I have done part a, I have no idea on part b, here is my attempt,
  18. S

    How to find the maximum angle of a pendulum after a mass collides with it

    Homework Statement A 10g ball is fired at 6 m/s into a 280g pendulum. What maximum angle will the pendulum swing to if the effective radius of the pendulum is 28cm? Homework Equations How to find theta? The Attempt at a Solution I converted 28cm to 0.28m; 10g to 0.010kg; and 280g to 0.280kg...
  19. B

    Where will the pendulum land -- Probability Question

    Homework Statement Imagine a number line -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 A pendulum begins at -1 and then swings towards the LEFT or RIGHT. There is no knowing how fast the pendulum is traveling or how much energy it has but will only swing LEFT or RIGHT. (I) Need to work out the...
  20. Rodrigo Schmidt

    Pendulum with a sphere vs with a particle in its end

    So, I'm really bothered with something. Let's suppose there's a simple pendulum with a rigid sphere on it's end. In order to get the motion equations I thought we could use two approaches. One would be using rigid body dynamics (torque, moment of inertia ...), the other one would be using...
  21. B

    I What are the definitions of Jacobi Elliptic Functions?

    When doing a problem on a pendulum undergoing elliptical motion, I came across sn(z), which is apparently a "Jacobi Elliptic Function". When I looked into it further, I saw that these functions are essentially circular trigonometric functions but about an ellipse instead of a perfect circle. Can...
  22. S

    Drag force on a flat plat like a pendulum?

    Hi , please i want to know if i have flat plate (rectangle) but its fixed like pendulum (fixed from one end and free at the other end and can rotate around this fixed end) i want to know the drag force due to air on this plate?
  23. Alexanddros81

    The pendulum is released from rest with θ = 30deg

    Homework Statement 13.54 The pentulum is released from rest with θ = 30deg. (a) Derive the equation of motion using θ as the independent variable. (b) Determine the speed of the bob as a function of θ. The solutions given in the textbok are a) ##\ddot θ = -4.905sinθ rad/s^2## b) ##6.26\sqrt...
  24. Alexanddros81

    Calculate the angular velocity and angular acceleration (pendulum)

    Homework Statement 13.53 The tension in the sting of the simple pendulum is 7.5N when θ=30deg. Calculate the angular velocity and angular acceleration of the string at this instant. Homework EquationsThe Attempt at a Solution Is this correct?
  25. S

    Pendulum on the end of a rotating disk

    Homework Statement There's a pendulum with mass m and longitude L strapped to a disk with radius R that rotates with an angular velocity ω. Calculate the angle that the pendulum is shifted (Φ) depending on ω. You are given m, L, R, ω, g. Calculate Φ depending on ω. Little drawing (with my...
  26. S

    Is the centripetal force a projection of tension?

    Well, this might be the stupidest question ever, but whatever. I was just thinking about a problem where a pendulum is attached to something that spins around itself (image below) and thought that maybe Centripetal Force might be a projection of tension on a vector that is perpendicular to ω...
  27. W

    Simple pendulum - displacement increase

    <Moderator's note: Moved from a technical forum and therefore no template.> A simple pendulum of length l (supported by a light, rigid rod) is released from rest at a small angle to the upward vertical. Show that the time taken for the angular displacement to increase by a factor of 10 is...
  28. Pushoam

    Angular frequency of a physical pendulum

    Homework Statement For calculating angular frequency of a physical pendulum, I consider its center of mass motion. The COM motion is a simple pendulum motion. Considering a coordinate system whose origin is the pivot point. Then, the COM is the length of the corresponding simple pendulum. Is...
  29. A

    Difference between angular frecuency and velocity pendulum

    Hello! I hope someone could help me to solve mu doubt, I am very confused and I don't find answers in internet. My question is about pendulums. I know the angular frecuency of a pendulum is give by the equation w= sqrt(g/L). But also i know the angular velocity (also named with "omega") can be...
  30. B

    I with a Rigid Pendulum Calculation please

    I have a rigid body pendulum that is used to strike an object at the bottom of its swing. Ultimately I would like to know how much forced is the object being struck with. Could I do this with just knowing the velocity of the weight? I was thinking then I could get P=MV. Can someone please help e...
  31. B

    Speed of pendulum at certain angles

    I'm having no problem finding the maximum speed of a pendulum but I'm not sure when I move its start point and measure point. I would like to know the speed of a pendulum at 30 degrees that has been dropped at 140 Degrees. I'm just giving some numbers to explain that it is above the horizontal...
  32. Timothy Schablin

    Momentum of a Pendulum: Angular and Linear Changes

    If a pendulum swings in a given arc, because of gravity acting on it in the vertical direction, does the linear and angular momentums change since it is picking up velocity because of gravity?
  33. Taaha

    Pendulum time at any given angel θ, 0<=θ<=π/2

    I got stucked with a solution of a problem. I have a pendulum of r radius which is in G gravitational field. So the working acceleration on the bob is a function of the angle. That is Gcosθ. The mass of the bob = m The radius of the string of the pendulum = r Gravitational force is G. So the...
  34. H

    How Do You Solve Complex Pendulum Equations in Physics Homework?

    Homework Statement For number 3,4,5 https://s4.postimg.org/qbp3xzq65/IMG_1092.png https://s22.postimg.org/u220j60sx/IMG_1093.pngHomework Equations Centripetal force = m v^2/R T = centripetal force + w Sigma F = m.a The Attempt at a Solution Number 3. Find the v at D point using...
  35. Kaneki123

    Are the Reasons for Pendulum's Mass and Amplitude Independence Contradictory?

    Okay...The time period of a pendulum is independant of its mass and amplitude.For the "independance of mass",the reason is that, for same amplitude (distance from mean position), any change in mass would have no effect on the acceleration of the mass (gravitational acceleration is...
  36. P

    Impact of a elastic string on pendulum

    Hello All, I was performing an experiment in which the perod of oscllation of a pendulun at different lengths is measured using a light gate. while performing the experiment i noticed that the string was slightly elastic, differing from the perfect pendulum. I was attempting to figure...
  37. Schwarzenberger

    Student Questions on Forces for Forensic Anthropology Research | MSc. Project

    Hi everyone! I have few questions which I think might actually be simple, but I would like some confirmation if possible. Here's the situation: I am doing a research project for my MSc. in Forensic Anthropology. The goal of my project is to study the marks left on bones by bladed weapons (in...
  38. S

    Velocity, momentum and energy values for a Pendulum swing

    Homework Statement This is my 'carrying out a practical investigation' assignment for Maths. I've attached the coursework (what I've wrote up to now) and my main concern is whether I've got the right differential equation to find 3 new velocity values throughout the pendulum trajectory...
  39. K

    Simple Harmonic Motion/Period of a Physical Pendulum

    I'm studying the motion of a physical pendulum, could someone help me make the final step in figuring out how to find the period so I can make predictions before carrying out a practical? Basically I have a meter rule with holes drilled along the length and will be pivoting it at various points...
  40. sefiroths

    Java Runge-Kutta method for Simple pendulum in java

    Hi, I'm trying to study Runge-Kutta method and apply on a simple pendulum. Using a timestep dt=0.1 (h=0.1) the pendulum increses energy of 1% every period... while in this site: https://www.myphysicslab.com/pendulum/pendulum/pendulum-en.html decreses energy about 0.01% What am I doing wrong...
  41. saadhusayn

    Pendulum oscillating in an accelerating car

    We have a car accelerating at a uniform rate ## a ## and a pendulum of length ## l ## hanging from the ceiling ,inclined at an angle ## \phi ## to the vertical . I need to find ##\omega## for small oscillations. From the Lagrangian and Euler-Lagrange equations, the equation of motion is given...
  42. StudentOfScience

    Spring Pendulum with Drag: Newtonian and Lagrangian Approaches

    Homework Statement Consider a point mass of mass m suspended from an ideal, massless spring. Let ##\theta ## be measured from the vertical. Find the displacement of the mass as a function of time if the spring is initially stretched/compressed a distance ## l_0 ## and has an initial velocity...
  43. Physics Dad

    Equation of motion of a dampened pendulum

    Homework Statement Hi, I have the following question... A pendulum consisting of a mass of 1kg is suspended from a string of length L. Air resistance causes a damping force of bv where b = 10-3 N/m 1) Derive and solve the equation of motion 2) Calculate the fractional decrease in amplitude...
  44. B

    Mathmatical model of a pendulum

    Homework Statement Suppose the pendulum string is attached to a point on the ceiling 30 cm from the wall. The weight is moved away from its rest position and released at time t=0. At time t=1.4 sec, it reaches its maximum distance from the wall, 37.4 cm away, and then swings back toward the...
  45. Andrew Deleonardis

    I Lagrange Pendulum Equation of Motion

    Hi, I've derived the equation of motion for a regular single pendulum, but do not know how to solve the differential equation. I have the following: r2θ''2=mg(cosθ-rsinθ)
  46. N

    MATLAB Solving an Elastic Pendulum Equation with Matlab/Excel

    Hi guys, I need to transform Newtonian solution of motion equation for spring (elastic) pendulum into Matlab or Microsoft Excel. I want to use Euler´s Method (or Runge Kutta Method) of numerical solution for that problem. I know all the equations but I have a problem with making some code from...
  47. N

    Pendulum with spring instead of rod

    When we have solid rod instead of spring I can solve this problem in Microsoft Excel either with Euler´s method or Runge Kutta method, but that spring makes this problem hard for me.
  48. N

    Non-harmonic oscillation of pendulum

    Hi, I would like to ask what is the formula for non-harmonic oscillation of pendulum? I know that formula for harmonic oscillation of pendulum is: (d^2 φ)/(dt^2 )+g/r sinφ=0 where φ is angle, t is time, g is gravitational acceleration, r is length of a rope. I know that harmonic oscillation...
  49. F

    Differential equation for a pendulum

    Homework Statement A simple pendulum is formed by a light string of length ##l## and with a small bob ##B## of mass ##m## at one end. The strings hang from a fixed point at another end. The string makes an angle ##\theta## with the vertical at time ##t##. Write down an equation of motion of...
  50. F

    Modelling eddy currents in a pendulum

    Hello, I was solving a problem related to Eddie currents recently and I need some help with simulating it numerically. Basically, we have a disc-like copper pendulum entering a region of uniform magnetic flux density B (see diagram). I understand that I need to use Faraday's law: \nabla...
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