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timekeeper, used in homes and offices for 270 years, and achieved accuracy of about one second per year before it was superseded as a time standard by the quartz clock in the 1930s.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'.
Simple pendulum problem - having trouble with the math!
Homework Statement
A simple pendulum is set up on Mars where g=3.72m/s^2. How long should pendulum be if period T is to be 2.00 seconds?
Homework Equations
T=2pia(3.14) times square root of l(length)/gravity
The Attempt at a...
HI ALL!
Im new to physics forums, so ill see how i go :)
I have some questions below regarding a simple pendulum:
1) Why does the string need to be massless? What will happen if it isn't massless?
2) What does a "frictionless pivot mean"? If i have two plates which have the string in...
I know this is probably a dumb question, but it's a long time since I did basic mechanics.
Consider a simple pendulum, consisting of a weight suspended a hook on the ceiling by a string. Say the pendulum is moving in a plane, so that its motion can be described by one coordinate theta as a...
Homework Statement
Textbook question: We know that the pendulum will eventually stop swinging. Explain what happens to the mechanical energy of the pendulum system.
Homework Equations
None needed.
The Attempt at a Solution
I know that when the pendulum is first released from rest...
1. Write the equation of motion for the pendulum for different lengths. Use the motion at its greatest extension when t=0 and find the phase shift.
I am supposed to find the equation of motion (x=xmax cos(\omegat+\phi) where xmax is the amplitude, \omega is the angular frequency, and \phi is...
Homework Statement
[PLAIN]http://img825.imageshack.us/img825/2673/58894277.png
Homework Equations
sin(theta) ~ theta for small angles.
The Attempt at a Solution
I'm having a hard time understanding what the question is asking since I don't have a lot of experience in stability...
Homework Statement
The relationship between velocity and position of a simple pendulum is given by the equation y= \pm\sqrt(2(C+\omega^2 cos x)). The corresponding phase diagram is attached. How on Earth did they come up with the phase diagram. How do you plot such a complicated equation...
Homework Statement
A 100g pendulum bob hangs from a 1 meter string. What is the tension in the string when the pendulum is not moving (i.e. at the 'bottom')? What is the tension when it is at 30° to the vertical?
Homework Equations
100g=.1kg
g=-9.8m/s^2
F_t=-mgcos(Θ)
The Attempt at a...
Aim: To measure the acceleration due to gravity using a simple pendulum.
source of error
1. The length of thread between the bob and the coins is not measured by very accurate instruments. Since meter ruler has a large percentage error, as a result, it should be replaced by a vernier caliper...
Homework Statement
Derive a formula for the maximum speed V_max of a simple pendulum bob in terms of g, the length l and the maximum angle of swing Θ_max. (Hint: Use the fact that the same amount of energy at the top of the arc is the same as at the bottom of the arc.)
The picture depicts...
Homework Statement
A simple pendulum of length (1.0m) and mass (5.0*10^-3 kg) is placed in a uniform electric field that is directed vertically upward. The bob has a charge (-8*10^-6 C). The period of the pendulum is (1.2 s). What are the magnitude and direction of the electric field...
Homework Statement
A simple pendulum is 5.20 m long. What is the period of simple harmonic motion for this pendulum if it is hanging in an elevator that is accelerating upward at 5.90 m/s2?
Homework Equations
T=2pi*(sqrt(L/g))
The Attempt at a Solution
all I did was plug in the...
Homework Statement
Trying to create an excel spreadsheet that outputs the angles of a simple pendulum as it slowly comes to a stop.
Homework Equations
so I've used the formula:
θ(t) = θ0cos(squareroot(g/R*t)
where:
θ0= inital angle
g=gravity constant
R= length of string
t=time...
Homework Statement
A simple pendulum of mass 19 kg is displaced an angle of 13 degrees from vertical and released. It now has a period of 2 sec.
a) Its mass is doubled. What is its period now?
T2m = 2 sec
b) Its length is doubled. What is its period now?
T2L = 2.828 s
c) What if...
Homework Statement
A simple pendulum oscillates with frequency f. What is its frequency if it accelerates at 0.50g upward
Homework Equations
f = 1/2pi sqrt(g/L)
The Attempt at a Solution
I want to say that g in the equation is equal to 0.50g, but I know this is wrong. Why do...
1. To Find The Height Of a Room by an Experiment using Simple Pendulum
MATERIALS REQUIRED
A simple pendulum, metre scale, stop clock, bobs of different masses, wooden blocks, a long string which has greater than the height of the laboratory.
INTRODUCTION
The period of a simple pendulum...
Simple pendulum is said to be not applicable if it's in the space that far from other planet which there're no gravitational field present.
Howerver when the system is inside a free falling lift, isn't the bob of the pendulum experience an accelration with value equals to g?
Is it correct to...
1. Homework Statement :
A simple pendulum has a mass of 0.25 kg and a length of 1.0 m. It is displaced through an angle of 5.0° and then released.
1. What is the maximum speed?
2. What is the maximum angular acceleration?
Answer: 0.855 rad/s2
3. What is the maximum restoring force?
Answer...
in this simple pendulum there are 3 points A,B,C , at point A the displacement is 0 , at point B the displacement is maximum and at point C what is the displacement??
also
When the Pendulum starts from maximum Displacement i.e point B , the velocity at point B would be 0, and at point A the...
A simple pendulum of length L and mass m swings about the vertical equilibrium position (θ=0) with a maximum angular displacement of θ_max. What is the tension in the connecting rod when th pendulum's angular displacement is θ=θ_max?
i drew a free body diagram and using simple geometry with...
Homework Statement
I searched and got nothing, I am also new here as my friend recently introduced me to this forum last night. I have gotten every single problem correct except this one so here goes:
A 300 g mass on a 1.0 m long string is pulled 8.8° to one side and released. How long...
Homework Statement
We push a weight hanging on a long string in a horizontal direction so that the velocity at the beginning is v = 10 cm / s. What is the oscillating time of such a pendulum, if the string on which hangs deviates the most for θ = 5 º?
Homework Equations
T = 2pie[sqrt(L/g)]...
For the simple pendulum lab, I have to find the percent difference between my theoretical and experimental velocity. I found out my theoretical velocity as I used the conservation of energy to generate an equation for v, but I'm having a hard time calculating my velocity from my experimental...
Homework Statement
A pendulum with a swing amplitude of 150 cm is recorded to have a period of 2.1s. Calculate after 0.3s release from the furthest amplitude position.
a) Angular velocity
b) displacement
c) Angular acceleration
d) Length of the pendulum
I've only had one lecture on...
Homework Statement
The motion of a simple pendulum is only approximately simple harmonic. How small should the amplitude should be for the approximation to hold good?. Obtain the general expression for the time period of a simple pendulum. How much does the actual time period differ from the...
I'm wondering this because my textbook says that for small angles it is, but we learned that for simple harmonic motion to occur there must be a linear restoring force.. eg F= -kx.. but for the simple pendulum the restoring force is F= -mgsin(theta).. wouldn't this not be linear?
I'm trying to write a program to model a simple pendulum, and I'm having some trouble seeing how I would solve for the position w.r.t. time.
I would ultimately like to be able to specify a length of string, acceleration due to gravity, mass (though I know it has no effect on the period) and...
How to find "g" using a simple pendulum?
We just started physics in grade 11.
I have no idea of how to find g using a pendulum.
This a lab we will have to do soon in the near future
I am here to do some research before we have to do the lab.
I've done some other research on the net, and i came...
Homework Statement
I need all the variables that causes the pendulum to stop.
Homework Equations
The Attempt at a Solution
I know friction causes the pendulum to stop but what type of friction is it and what from?
thanks
A uniform disk of radius 0.2m and 5.6 kg mass has a small hole distance d from the disk's center that can serve as a pivot point. What should be the distance d so that this physical pendulum will have the shortest possible period? What will be the period at this distance?
So, I know that the...
Homework Statement
Is there an actual formula for the acceleration of a simple pendulum.
I know that the distance is angular displacement=angular amplitudesin(wt+phase constant) and the velocity is angular velocity= Length of String* w*angular amplitude cos(wt+phase constant)
Homework...
I am working on my lab report for the simple pendulum and we did an experiment where we increased the max theta in increments of 5 degrees, while keeping the length of the sting the same. We started from 5 degrees and went to 45 degrees. For some reason the periods seem to increase slighty as...
I was just wondering where this comes from. Our professor was giving a lesson on the simple pendulum in the lab class. I copied all of the equations and how he manipulated then I understood, except for this part. I forgot to ask after class, but if you can explain it or want more relative...
Homework Statement
1. A simple pendulum of length L is attached to a cart that slides without friction down a plane inclined at angle theta with the horizontal. Find the period of oscillation of the pendulum on the sliding cart.
2. A clock with a pendulum keeps perfect time on Earth's...
Homework Statement
A pendulum has a period of 1.8 s.
Homework Equations
Its length is doubled. What is its period now?
The original pendulum is taken to a planet where g = 16 m/s2.
What is its period on that planet?
The Attempt at a Solution
T=2pi sqrt(L/g)
1.8=2pi...
Homework Statement
A simple pendulum has a mass of 0.250 kg and a length of 6.00 m. It is displaced through an angle of 10.0° and then released. Solve this problem by using the simple harmonic motion model for the motion of the pendulum.
(a) What is the maximum speed?
(b) What is the...
A simple pendulum consists of a mass m tied to a string. It swings freely within the limits indicated in the figure below. On a swing from left to right, the string is cut suddenly just as the pendulum is vertical. Select the letters that show the path of m, the direction of the force right...
As I've posted before, I teach an acoustics lab to undergraduate physics students and, they are currently working on an experimental observation of the motion of the simple pendulum.
How does the motion of a simple pendulum relate to music?
Everyone who has replied to any of my threads...
Homework Statement
I'm new to this forum and I'm not very sure with how I'm suppose to state my problems, thus if it's written wrong please tell me so.
I'm currently doing a motion lab report for my physics class and we have to analyse the motion of a pendulum.
The material used for the...
Homework Statement
Pathria 2.6 (2nd Edition): Phase space volume of a simple pendulum.
The total energy can be expressed in the form of the time derivative of the angle + the Sin^2 of that angle.
From this I want to calculate the phase space volume. Mathematica gives the solution in the...
Homework Statement
A pendulm bob weighing 0.1 kg hangs from a light tread. it has a length of 25 cm and a period is 1 second and the force is 1.1 N. what is the maximum velocity of the pendulum bob?Homework Equations
F = M * A
V = U + A*TThe Attempt at a Solution
Using these formulas i got the...
Homework Statement
A simple Pendulum is suspended from the ceiling of an elevator. The elevator is accelerating upwards with acceleration a. The period of this pendulum, in terms of its length L, g, and a is:
2\pi*(L/a)^(1/2)
OR
2\pi*(L/(g+a))^(1/2)
OR
2\pi*(L/g)^(1/2)
Homework...
For a simple pendulum practice with clamp, boss head and resort stand assembled, also a string attached to the end of clamp and a bob, then swings it and measure the time for it to complete a period.
At the end use the information collected to calculate acceleration due to the gravity by the...
A simple pendulum has a period of 2 s for small amplitude oscillations.
1. The length of the pendulum is most nearly
(A) l/6 m
(B) ¼ m
(C) ½ m
(D) 1 m
(E) 2 m
I used the period of a pendulum equation, did some algebra, and got D as the answer. Is this correct?
2. Which of...
Homework Statement
Using the usual angle \phi, as generalized coordinate, write down the Lagrangian for a simple pendulum of length l suspended from the ceiling of an elevator that is accelerating upward with constant acceleration a. Find the Lagrangian equation of motion and sho that it is...
Homework Statement
The diagram shows a simple pendulum consisting of a mass M suspended by a thin, massless string. The magnitude of the tension is T. The mass swings back and forth between +/- θ0. Select all correct answers, e.g. B, AC, BCD.
A) T is largest at the bottom (θ = 0).
B) T...
Simple pendulum question.. help needed!
http://capa.mcgill.ca/res/mcgill/dcmcgill/oldproblems/msuphysislib/Graphics/Gtype26/prob34a_pendSHM1.gif1.[/URL] The diagram shows a simple pendulum consisting of a mass M suspended by a thin string. The magnitude of the tension is T. The mass swings back...