Pendulum Definition and 1000 Threads

Homework Statement My problem/task is to explain in elementary terms the dynamics of a string coupled pendulum, the same as in this diagram: Is it simple to make a free body diagram for the pendulums? Is it possible to understand the motion as being caused by SHM oscillation of the top...

Hi everyone! I recently came across the Lyusternik-Fet theorem concerning closed geodesics on a compact manifold. For simplicity of description, take the 2-torus, and imagine it represents the configuration space of a double pendulum. For every pair of integers m, n (where m represents the...

Homework Statement This could be a more general question about pendulums but I'll show it on an example. We have a small body (mass m) hanging from a pendulum of length l. The point where pendulum is hanged moves like this: \xi = A\sin\Omega t, where A, \Omega = const. We have to find motion...

how do the two different masses (wooden and metallic) at the ends of the pendulum help?

Hi community, The phase relationship is 0 for the shorter pendulae, 1/4 cycle for the pendulum in resonance and in anti-phase for the longer pendulae; relative to the driver pendulum. I have observed this but I can see it conceptually to an extent but wondered if anyone knows of a resource for...

Hi good day. I am trying to find the general Inverted Pendulum on a cart nonlinear state space equations with two degrees of freedom with x, x_dot, theta, theta_dot which represents displacement, velocity, pendulum angle from vertical, angular velocity. However from research, I am seeing...

Homework Statement Consider a rod of length ##L## and mass ##M## attached on one end to the ceiling and on the other end to the edge of a disk of radius ##r## and mass ##m##. This system is slightly moved away from the vertical and let go. Let ##\theta## be the angle the pendulum makes with the...

Homework Statement In the figure attached, what is the torque about the pendulum's suspension point produced by the weight of the bob, given that the mass is 40 cm to the right of the suspension point, measured horizontally, and m=0.50kg? Homework Equations tau = rFsin (theta) or tau = lF...

Hi, If I find out the tangential force on the bob at position 1, it turns out to be m*g*sinθ. From this if I find out acceleration by dividing this equation by m, I get only g*sinθ. Does it mean the max acceleration of pendulum has got nothing to do with its length or mass but theta?

I have trouble with finding the eigenstates of a spherical pendulum (length $l$, mass $m$) under the small angle approximation. My intuition is that the final result should be some sort of combinations of a harmonic oscillator in $\theta$ and a free particle in $\phi$, but it's not obvious to...

Homework Statement I am trying to learn how to create state space representations. I am using this link to study. http://www2.ensc.sfu.ca/people/faculty/saif/ctm/examples/pend/invpen.html Could someone explain how to get the matrix A from my equations? Homework EquationsThe Attempt at a...

Is the simple pendulum considered to be an example of oscillatory motion or periodic motion or both?

Hi. I have a spring with spring constant 30 N/m and a mass of 0.5 kg. With the mass at the bottom, the spring has the length 58 cm at rest. If I now pull down the mass and release it, it starts with a vertical oscillation, then the spring also starts to swing sideways like a pendulum and the...

I have been doing pendulum problems lately, and I have found 2 different formulations for potential energy of a pendulum. U=mgl(1-cos(Θ)) and U=-mglcos(Θ) The first says U=0 when Θ=0 (at the bottom). The second has U=0 when Θ=π/2 (halfway to the top). Both give the same equation of motion...

Dear Community, I am trying to implement the inverted pendulum cart simulation. To do so I’ve used the equation system 5 published here http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.619.551&rep=rep1&type=pdf I've solved the equation by left hand multiplication with the inverse which...

Hello, I have recently been introduced to the topic of simple harmonic motion for the first time (I'm currently an A-level physics student). I feel that I have understood the fundamental ideas behind SHM very well. However, I have one question which has been bugging me and I can't seem to find a...

Homework Statement The pendulum cord is released from rest when the angle = 0 (from a horizontal) If the string breaks when the tension is twice the weight of the bob at what angle does it break? Im from NZ and our NCEA system is often riddled with mistakes and I want to clear this up. Is the...

The coordinates of the mass 'm' is $$x=R\cos(\omega{t})+R\cos(\omega{t}+\phi)$$ $$y=R\sin(\omega{t})+R\sin(\omega{t}+\phi)$$ Where $\phi$ is the angle of the particle with respect to coordinate system attached to the circle with origin at center of the circle. Since particle is not acted upon...

For the experiment, we were to determine the relationship between two quantities through linearization after collecting measurements. To verify that P~L^1/2. and determine proportionality constant, C. P=C√L/g= (Cg^-1/2)(L^1/2) Materials used were a timer, string(The pendulum on length), and a...

Homework Statement Use unit analysis to show that the constant, 2π, is unitless. Homework Equations T=2π√L/g[/B] The Attempt at a Solution T= [T] L= [L] g= a= [L]/[T]^2= [L T^-2] [T]= 2π√[L]/[L T^-2] [/B] Is this correct? I wasn't really sure how to do this. I'm using book examples to...

I know that I'm rushing too much but I wanted to see if I can calculate the work of a pendulum that does oscillation with a similar way you calculate the work of a spring. Consider the following free body diagram: Things i noticed: 1) The position is changing both in x and y-axis while the...

Homework Statement A pendulum with a light rod of length ##l## with a bob of mass ##m## is released from rest at an angle ##\theta_0## to the downward vertical. Find its angular velocity as a function of θ, and the period of small oscillations about the position of stable equilibrium. Write...

Homework Statement A pendulum of mass ##m## and length ##L## is connected to a spring as shown in figure. If the bob is displaced slightly from its mean position and released, it performs simple harmonic motion. What is the angular frequency of the bob? Homework Equations Angular frequency for...

Homework Statement A solid rod of length L and mass M has a pivot through its center and is originally horizontal. Another mass 2M is then attached firmly to one end of the rod, and released. What is the maximum speed of the mass 2M attained thereafter? (Cornell 2009) Homework Equations Not...

Is this some esoteric aspect of Physics, that few ever see, or is this part of the common core that almost every Physics major sees? http://scienceworld.wolfram.com/physics/DoublePendulum.html

Homework Statement Is the time average of the tension in the string of the pendulum larger or smaller than mg? By how much? Homework Equations $$F = -mgsin\theta $$ $$T = mgcos\theta $$ The Attempt at a Solution I'm mostly confused by what it means by time average. However from my...

Hey all, I started building my own flywheel inverted pendulum (i'm using a standard PID controller for the balancing). I came across many articles regarding the differential equation of the pendulum. Most article develop the motion equation using the Euler–Lagrange, few chose the Newtonian way...

Hi, I need a simple way to measure the maximum angle/vertical displacement of a 3D pendulum (weight hanging from a rope) undergoing random impacts. What will work?

Hello, my name is Django and I live in the Netherlands. I've got an assignment for physics about pendulums and part of this assignment is that I need to verify my result with someone else in a country with a different gravitational force (the gravitational force were I live is 9.813 N/m2). I...

Homework Statement [/B]Homework EquationsThe Attempt at a Solution Sir if the pendulum is given an angular velocity about the -he z axis then whether eq 1 is right for balancing force and I have a contradict regarding eq 2 and eq 3[/B]

Hi there. I am working on some exercises where they ask about the steady state of a pendulum. I have had quantum mechanics, where the steady state meant a time independence. But I don't really see what this means for a pendulum. Is it steady when it's velocity is zero so there is no time...

Hi there. I have a question about the damped pendulum. I am working on an exercise where I have already numerically approximated the solution for a simple pendulum without dampening. Now, the excercise says that I can simply change the code of this simple situation to describe a pendulum with...

I'm about to pick up again on a project started last summer to build a Foucault pendulum that will fit on, or at least, above a desk in an ordinary room. This was described, with photographs in...

Hi, I was pondering a question after seeing a video about chaotic magnetic pendulums. If you were to suspend a magnet on a pendulum above a repelling magnet, would it stop moving or would you get perpetual motion? My guess is it would stop moving but I can't think of how. Gravity would try to...

Homework Statement Homework Equations U = (1/2)kx^2 T = 2 * π * (m/k)^ (1/2) The Attempt at a Solution [/B] I said that the angular velocity is w = (2 * π) / t And the equation for velocity would be: v(t) = -Aw * cos (w * t) However, I don't know how to relate this to the speed at...

Homework Statement Is the tension in the string of a pendulum, when averaged over time, larger or smaller than the weight of the pendulum? Quantify your answer. You may also assume that the angular amplitude of the oscillations is small. Homework Equations For tension ##T##, angular...

Homework Statement A torsional pendulum consists of a disk of mass 450 g and radius 3.5 cm, hanging from a wire. If the disk is rotated through an angle of 45o and released from rest and oscillates with a frequency of 2.5 Hz, what is the torsion constant of the wire? A : 1.7 x 10-3...

Homework Statement [/B] In a homogeneous gravity field with uniform gravitational acceleration g, a pointmass m1 can slide without friction along a horizontal wire. The mass m1 is the pivot point of a pendulum formed by a massless bar of constant length L, at the end of which a second...

Homework Statement The picture illustrates a simple pendulum and and two physical pendulums ,all having the same length ,L. Class their period in ascending order. Homework Equations T = 2π / ( I/mgh) I = Icm + mh2 Icm=(ML2/12) The Attempt at a Solution I have found the period for first...

Homework Statement A 110 kg panda is riding on a 3.0 m long swing whose mass can be considered negligible. The highest point of its arc occurs when the swing makes a 20° angle with the vertical. What the magnitude of the total tension in the ropes of the swing at that point? m (mass of panda)...

Good afternoon people. I wanted to implement a physical system using control just to put into practice what I have learned in school. To be more specific: I would like to implement an inverted pendulum like the one on the photo In this system a control input (a force u) drives the cart (mass...

A torsional pendulum made by suspending a horizontal uniform metal disk by a wire from its center. If the disk is rotated and then released, it willexecute simple (angular) harmonic motion. Suppose at t seconds the angular displacement of \theta radians from the initial position is given by the...

Homework Statement The question is in the attached document Homework Equations Newton's second law states that F=ma Charged particle in magnetic field experiences F=Q ( v X B) The Attempt at a Solution Since the charge 'Q' is constrained to move along a path in xy-plane in such a way that the...

The Problem So, I know the basic, the basic differential equation of movement in terms of the angle it is formed, which has the form: 0 = g⋅sin[α(t)] + α''(t)⋅l. However, I decided to consider the friction force of the air, which is always contrary to the movement, and proportional to the...

Hey Wizards, I recently built a Reverse Hyper, picture attached, for my home gym. It's a basic pendulum on which weight is added. It currently utilizes 2 - 5/8'' pillow block bearings for the pivot. Each are rated to ~6.25 KN. Can anyone provide me with the equations or reference material, so...

Homework Statement I have found a differential equation that models a non-linear pendulum with air resistance, and now I have data. I've looked at the following site for guidance on how to analyse the data. It compares the motion of a damped spring, and compares it to the motion of a damped...

Homework Statement I found an answer on the internet for this problem, but I'm not sure on one of the steps. The solution says, "Take ln of both sides to get rid of Ae. If we do that, then the right side will be ln(Ae^t/T). I don't see how using ln will get rid of Ae? Homework Equations Refer...

Homework Statement The question is in part 3 (image). Basically I used the formula for Period, T, of a pendulum of length L with free-fall acceleration g. I got 8.52, but I had to further divide this number by 4 to get the time the person must hang on in order to drop into the water at the...

A motor drives a pendulum at its natural frequency and keeps it swinging at a constant rate. If this motor uses a longer pendulum, does a frequency need to be increased or decreased? I'm assuming that the question is asking whether or not the frequency that the motor drives a pendulum needs to...

1. Homework Statement The first astronauts to visit Mars are each allowed to take along some personal items to remind them of home. One astronaut takes along a grandfather clock, which, on earth, has a pendulum that takes 1 second per swing, each swing corresponding to one tick of the clock...