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timekeeper, used in homes and offices for 270 years, and achieved accuracy of about one second per year before it was superseded as a time standard by the quartz clock in the 1930s.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'.
For SHM of oscillating pendulum, when the pendulum is at the extreme position, what is considered as the displacement? The curve/arc of the circle the bob is following or the straight line distance from the mean position?
I want to investigate the phenomenon of Chaos in the form of how its driving amplitude affects _____, in a driven, damped pendulum, using a computer simulation given.
Initially I was looking at 'degree of chaos' for the dependent variable - to measure this I wanted to use the Lyapunov...
1. Two small spheres with masses m1 and m2 hang on weightless, insulating threads of length L1 and L2. The two spheres carry charges of q1 and q2 (like charges) respectively. The spheres hang such that they are at the same level with one another. The threads are inclined at angle theta 1 and...
Homework Statement
Give governing equations for the system about its static equilibrium, assuming small vibrations
System consists of two springs located under 45 degrees to the vertical (both have same k-value) in undisturbed situation. Lower ends of the springs are attached to each other...
Homework Statement
You are at a furniture store and notice that a grandfather clock has its time regulated by a physical pendulum that consists of a rod with a movable weight on it. When the weight is moved downward, the pendulum slows donw; when it is moved upward, the pendulum swings faster...
There is an swinging metal pendulum. I put one polar of bar magnet below the equilibrium. What will be the effect of the intensity of the magnet to the time taken for the pendulum to stop? Please explain the theory specifically since I am quite confused. Thank you very much.
Hello!
I'd like to ask for help with one problem :) thank you in advance.
1. Write the equations for kinetic and potential energy for the pendulum with rectangular prism of size a*b*c (width, length, depth). With the Lagrange's equation get the equation of motion. The block is homogeneous...
I have written a C program to trace out the motion of a double pendulum, but am having difficulties in getting gnuplot (controlled from my c program) to trace out the paths of the masses (example video below). Thus far I have created the program such that it produces a number of png images at...
Hello there. Recently I was tasked to design a lab experiment using a ballistic pendulum.
Now I understand that all the sources of the internet say that by principle of conservation of linear momentum,
(1/2)(m+M)V2 = (m+M)gh , or V2 = 2gh
And then using principle of conservation of energy, we...
Hello, everybody.
This website and many others define the potential energy of a double pendulum as:
V=-(m_1+m_2) g l_1 cos\theta_1-m_2 g l_2 cos\theta_2
However, I came up with the following equation:
V= (m_1+m_2) g l_1 (1-cos\theta_1)+m_2 g l_2 (1-cos\theta_2)
I started from the position...
Homework Statement
A clock is regulated by a pendulum. The pendulum can be considered as a small weight connected to a rod of negligible mass. The period of oscillation of the pendulum can be adjusted by moving the weight up or down the rod. The angular frequency is given by ##\omega ^2...
I am considering a simple inverted pendulum system given in the following page;
http://ctms.engin.umich.edu/CTMS/index.php?example=InvertedPendulum§ion=SystemModeling
System has two degree of freedom but the control input can be only applied as force to the chart. I am not sure about the...
Homework Statement
A metal rod of length 'L' and mass 'm' is pivoted at one end. A thin disk of mass 'M' and radius 'R' (<L) is attached at its centre to the free end of the rod. Consider two ways the disc is attached :
Case A: The disc is not free to rotate about its centre of mass, the...
Homework Statement
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In the overhead view of the figure, a long uniform rod of mass m = 0.24 kg is free to rotate in a horizontal plane about a vertical axis through its center. A spring with force constant 240 N/m is connected horizontally between one end of the rod and a fixed wall. When...
What is the minimum horizontal force "F" required to hold a simple pendulum (mass "m") with string of length "l" at an angle of 60 degrees with the vertical. [ given answer = mg/√(3) , veracity uncertain ]This at first seemed simple enough, standard mechanics apply, leading to ...
I am struggling with setting up a problem to solve for the change in amplitude of a pendulum affected by a damping force (presumable air friction) over a time period.
The original amplitude of the pendulum is 1.4 m from the equilibrium on a 15 m massless wire with a 110 kg brass bob at the end...
Homework Statement
Problem statement -
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Klepner and Kolenkow 6.15 : A pendulum is made of two disks each of mass M and radius R separated by a massless rod. One of the disks is pivoted through its center by a small pin. The disks hang in the same plane and their centres are a distance l...
I am newly learning Lagrange formalism and I learned how to get the equation of motion for a simple pendulum using Lagrange in the spherical coordinate system. But I am unable to derive the same using the Cartesian system. If someone can please tell me what is wrong with the following...
Consider a realistic pendulum with a bob of mass ##M## and a rod of mass ##m##. For the purposes of torque, is it correct to treat the bob and rod as two separate point masses, one at length ##L##, and the other at length ##\frac{L}{2}##?
When I implemented this idea, I found that centripetal...
Homework Statement
My textbook states that for oscillations of pendulums, the restoring force is ##F = -mgsin(\theta)##. "Because F is proportional to the sine of ##\theta## and not ##\theta## itself, the motion is not SHM (simple harmonic motion)". I don't understand the last sentence...
Homework Statement
In the Cavendish experiment, the two small balls have mass m each and are connected by a light rigid rod with length L. The two large balls have mass M each and are separated by the same distance L. The torsion constant of the torsion wire is κ.
b) Put the large balls a small...
The sistem above is the one I'm interested in. There is two equally charged spheres spinning on a plane. The line has L=\sqrt{2} m and the spheres weight 0.6Kg. The angular speed is \omega = 2rad/s.
The radius for the circular trajectory is R=1m and so the centripetal force is...
Homework Statement
This is a 'random discussion' that I had today with a student; it is not out of a textbook, nor does the solution carry any weight at all (pls excuse pun).[/B]
A simple pendulum is happily swinging back and forth attached to a pin in the wall of the lift, where the pin is...
Homework Statement
A simple pendulum with bob of mass m and conducting wire of length L swings under gravity through an angle 2 theta. The Earth's magnetic field component in the direction perpendicular to swing is B. The maximum potential difference induced across the pendulum is
Homework...
Homework Statement
I'm doing an EPI on horizontal circular motion and for one test the independent variable is mass and I need to control the velocity by using the 2πr/T formula. So I know how to use the forumula to find an unknown but how do I use it for two unknowns (r and T). Is there a...
Homework Statement
I want to sum the forces perpendicular to the pendulum and sum the moments about the pendulums center of gravity.
Homework EquationsThe Attempt at a Solution
P\sin \theta - mg\cos \theta - N\cos \theta = -m\ddot x\cos \theta + ml\ddot \theta
-Pl\sin \theta - Nl\cos \theta +...
In the included picture, I don't get how they get to the kinetic energy part. I would say, that the traveled distance is equal to (l + x(t))*θ. Then I would take the time derivative, resulting in dx(t)/dt * θ + (l + x(t))* dθ/dt. Then I would square this result and multiply that with 1/2 m. But...
Ok guys so for my lab report I am given an equation of period=2pi(length/a)^b and through this equation and the slope and y-int of my log-log graph I am suppose to solve for the values of a and b. I know that taking the log of the equation gives me log(T)=log(2pi)+blog(L/a) and this relates to...
Kinetic Energy of Double Compound Pendulum and Parallel Axis Theorem
Hello, there.
I have a project I'm working on where I need to be able to calculate the kinetic energy of what basically amounts a double compound pendulum. However, the pivot point of the second pendulum is not at the center...
I was waiting for the http://mathhelpboards.com/potw-university-students-34/problem-week-156-march-23-2015-a-14734.html for University students solution to be posted before I asked this question. I ran across this problem as I was trying to solve the problem and I got stuck rather quickly.
The...
Homework Statement
We have a light rigid pendulum with length ##l##. A mass ##M## is placed at the end and a mass ##m## is placed a distance ##x## from the pivot. What is the period of the pendulum?
Homework EquationsThe Attempt at a Solution
Reduce the problem to a single mass situation...
Homework Statement For the conservationofenergy,calculate the starting height of the bob. This is done with some trigonometry and is
∆h=L−Lcosθ
Calculate the initial potential energy of the pendulum for each of your starting angles.Now, using the diameter of the hanging mass (2 cm),and the time...
In a discussion with someone claiming to be a physicist (whether PhD or something less he did not say) we got into a hypothetical discussion related to Hitchhiker's Guide to the Galaxy. An alien civilization wants to move the Earth out of the way because it's impeding a galactic highway...
Hi Clever People,
Is there any method or gyro to prevent pendulum motion of an object when lowering it using a cable and a winch? I am doing a home projects and the motion is a big problem.
Thank you in advance.
Homework Statement [/B]
Find the Cartesian coordinates (x, y, z) of a fixed reference frame expressed in terms of the coordinates (x', y' , z) of a rotating frame, which rotates with the horizontal rod HR. Choose the x' -axis to point along the horizontal rod in the direction OA.
Use this to...
Homework Statement
Derive Newton's and Lagrange's equation of motion for the system. Discuss differences and show how Newton's equations can be reduced to lagrange's equations. Assume arbitrarily large θ.
The system is a pendulum consisting of a massless rod of length L with a mass m...
Homework Statement
Derive Newton's and Lagrange's equation of motion for the system. Discuss differences and show how Newton's equations can be reduced to lagrange's equations. Assume arbitrarily large θ.
The system is a pendulum consisting of a massless rod of length L with a mass m...
Homework Statement
A compound pendulum consists of a thin rod of length 1.4 m and a disc of radius 0.2 m. The centre of the disc is attached to the end of the rod and the pendulum pivots about the opposite end of the rod. Both the mass of the rod and the mass of the disc are the same, each...
In the book "Introduction to Mechanics" by K&K, in the section on conical pendulums, the net force in the ##\hat{k}## direction is set to zero, since the ##z##-coordinate of the particle doesn't change. However, later on the effect of changing ##\omega## on ##\alpha## (the angle the rod makes...
Homework Statement
A long light inflexible rod is free to rotate in a vertical plane about a fixed point O. A particle of mass m
is fixed to the rod at a point P a distance ℓ from O. A second particle of mass m is free to move along the rod, and is attracted to the point O by an elastic force...
Homework Statement
For a double pendulum, how do we plot the phase space for ##\theta_2## (the lower of the pendulum), i.e. the plot ##\theta_2, \ \dot{\theta}_2?##
##x## = horizontal position of pendulum mass
##y## = vertical position of pendulum mass
##\theta## = angle of pendulum (0 =...
Homework Statement
Hi, I need help in solving question c) (a pendulum) The required data, problem and relevant equation is in the pictureThe Attempt at a Solution
I am not sure how to solve it but here are my thoughts:
since mg is working at j
y(t)j= mg
does that mean K(r-L0) x(t) direction?
I...
I am having difficulties writing my damped oscillations lab report. We were asked to write a short essay on eddy currents (creation,direction advantage and disadvantage) and their relationship with torsion pendulums. Also,we have to explain if the copper wheel in the torsion pendulum could be...
Homework Statement
Hey guys, so I'm doing the an exercise on the Kater's pendulum, to calculate g. I've gotten down my g calculation to g = 9.80658m +/- 0.00054 using equation 1 below. The errors taken into account are just on the kater period T and the distance between the two pivot points (L)...
Homework Statement
What length must the pendulum be changed to in order to show the correct time?
L=0.5m
After 12hours the clock is behind by 30minutes.
Homework Equations
w=sqrt(g/L)
w=2πf
The Attempt at a Solution
I thought if I set the frequency equal to 1Hz and solved for length it would...
I just recently worked through the lagrangian method for describing the motion of a double pendulum. What I want to do now is describe the motion of a double pendulum that has been instantaneously released from the origin and allowed to fly through the air (with the 2 pendulums still connected...
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...
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...
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...