What is Harmonic motion: Definition and 1000 Discussions
In mechanics and physics, simple harmonic motion (sometimes abbreviated SHM) is a special type of periodic motion where the restoring force on the moving object is directly proportional to the object's displacement magnitude and acts towards the object's equilibrium position. It results in an oscillation which, if uninhibited by friction or any other dissipation of energy, continues indefinitely.
Simple harmonic motion can serve as a mathematical model for a variety of motions, but is typified by the oscillation of a mass on a spring when it is subject to the linear elastic restoring force given by Hooke's law. The motion is sinusoidal in time and demonstrates a single resonant frequency. Other phenomena can be modeled by simple harmonic motion, including the motion of a simple pendulum, although for it to be an accurate model, the net force on the object at the end of the pendulum must be proportional to the displacement (and even so, it is only a good approximation when the angle of the swing is small; see small-angle approximation). Simple harmonic motion can also be used to model molecular vibration as well.
Simple harmonic motion provides a basis for the characterization of more complicated periodic motion through the techniques of Fourier analysis.
Homework Statement
I don't have a homework question exactly, but I need help with an equation please.
Angular frequency: W= 2 pi/T = 2(pi)(f) f= frequency
And- W = square root of (k/m) k = spring constant m= mass
So, wouldn't T = 2 pi / square root of (k/m) ??
My...
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A block, attached to a spring, is set into vertical oscillation with an amplitude of 25.0 cm and a frequency of 5.00 Hz. At t = 0.00 s, the block is 14.0 cm below the equilibrium position and is moving upwards. Assume that the displacement from equilibrium is given by
y...
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A block of mass m= 0.0750 kg is fastened to an unstrained horizontal spring whose spring constant is k= 82.0 N/m. The block is given a displacement of +0.120m, where the + sign indicates that the displacement is along the +x axis, and then released from rest.
a. What is...
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a 1kg block sliding a frozen surfaces collideds w/a horizontal spring w/a force constant of 2N/m. The block compresses the spring 4m fr. its rest position.
a.how long does it take to fully colmpress the spring?b. what wa sthe speed of the block at the instant of the...
The displacement, x= Acos(\varpit+\phi), repeats for every increase in 2pi. Why can't I make the above equal to Acos(\varpit+\phi + 2pi), and divide by cos. This gives \phi]=0. This is clearly wrong. Why?
And how does angular frequency apply to a mass on a spring anyways, it doesn't move in a...
Homework Statement
Two blocks (m = 1.22 kg and M = 8.73 kg) and a spring (k = 344 N/m) are arranged on a horizontal, frictionless surface, with m resting on top of M and the spring attached to a wall and M. The coefficient of static friction between the blocks is 0.42. Find the maximum...
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A loudspeaker diaphragm is producing a sound for 2.5 s by moving back and forth in simple harmonic motion. The angular frequency of the motion is 7.54 x 10^4 rad/s. How many times does the diaphragm move back and forth?
Homework Equations
angular freq. (W for...
Homework Statement
Ok here's the problem.. a little lengthy so bear with me :) (3 parts need help w/ last two)
Expectant parents are thrilled to hear their unborn baby's heartbeat, revealed by an ultrasonic motion detector. Suppose the fetus's ventricular wall moves in simple harmonic...
Homework Statement
A child with poor table manners is sliding his 240 g dinner plate back and forth in SHM with an amplitude of 0.110 m on a horizontal surface. At a point a distance 7.00×10−2 m away from equilibrium, the speed of the plate is 0.350 m/s
1.What is the period?
2.What...
1. Determine the value of the acceleration due to gravity on planet X if a pendulum having a length of 30.0 cm has a frequency of .70 hz on that planet?
2. Find the period of motion for a 200 gram mass vibrating on a spring having a spring constant of 4.0 n/m?
3. When a mass of 35.0 grams...
Homework Statement
Well it's actually a colection of questions that I'd like to know if I've got the right end of the stick in answering;
Data to work with (just making it up):
Period (T)
Mass (m)
Radius of disk (r)
Gravitational Accelaration (g) 9.81 ms-2
1) Say we have a disk...
Homework Statement
A 1.08 kg block is attached to a horizontal spring with spring constant 3650 N/m. The block is at rest on a frictionless surface. A 10.6 g bullet is fired into the block, in the face opposite the spring, and sticks.
What was the bullet's speed if the subsequent...
On The Student Room I saw a couple of guys looking at whether the rules for Simple Harmonic Motion at non-relativistic speeds (e.g. a = -w2y and so on) would work if the maximum velocity of the particle hits relativistic speeds.
Many Thanks
W101
Homework Statement
An object of unknown mass M is hung from a vertical spring of unknown spring constant k, and the object is observed to be at rest when the spring has extended by 14cm. The object is then given a slight push and executes SHM. Determine the period of this oscillation...
[SOLVED] Finding the Amplitude of a spring (Simple Harmonic Motion)
First post here at PF, so forgive me if I make a faux pas. I'm trying to study for an upcoming Physics test and I'm having a bit of trouble with this.
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A massless spring with spring constant 19 N/m hangs...
Homework Statement
A 20 cm long (L) wrench swings on its hook with a period of 0.90s. When the wrench hangs from a spring of spring constant 360 N/m (k), it stretches the spring 3.0 cm (x). What is the wrench's moment of inertia about the hook.
A diagram also shows that the centre of mass...
Homework Statement
An object in SHM oscillates with a period of 4.0 s and an amplitude of 10 cm. How long does the object to move from x = 0.0 cm to x = 6.0 cm?
Homework Equations
x(t) = Acos(ωt +φ )
The Attempt at a Solution
ω = π/2
Acosφ = 0 ⇒φ = ±π/2
Since object is moving...
Homework Statement
A machine part is undergoing SHM with a frequency of 5 Hz and an amplitude of 1.8 cm. How long does it take the part to go from x=0 to x=-1.80 cm ?
Homework Equations
x = Acos (ωt + φ)
The Attempt at a Solution
1.80 cm = 1.80 cm * cos (ωt + φ)
ω = 2πf = 2π*...
Homework Statement
Consider the four block-and-spring systems shown. Each block moves on a horizontal, frictionless table. The blocks all have the same mass and all of the springs are identical and ideal with spring constant k. At the instant shown, each block is released from rest a distance...
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A block of mass m rests on a horizontal table and is attached to a spring of force constant k. The coefficient of friction between the block and the table is mu. For this problem we will assume that the coefficients of kinetic and static friction are equal. Let the...
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A 300g oscillator has a speed of 95.4 cm/s when its displacement is 3.0 cm and 71.4 cm/s when it displacement is 6.0 cm. What is the oscillator's maximum speed?
Homework Equations
x = Acos(\omegat + \phi)
v = -\omegaAsin(\omegat + \phi)
vmax = \omegaA
v =...
\piHi everyone,
I hope you can help me out with the following question. I am mainly confused about the sign
Homework Statement
A block in SHM with T= 4.0 s and A=0.1 m. How long does it take the object to move from x=0 m to x= 0.06 m.
Homework Equations
x=Acos(wt + \phi)
w=2pi/T...
An object goes through simple harmonic motion with its position described as...
Homework Statement
An object undergoes simple harmonic motion with its position described by
x(t ) = 50sin (2piet/3)
C) when is Velocity first equal to 80 D) whe nis the Velocity next equal to 80...
Homework Statement
A particle is in simple harmonic motion along the x axis. The amplitude of the motion is xm.
When it is at x = x1, its kinetic energy is K = 5J and its potential energy (measured with U = 0 at x = 0) is U = 3J. When it is at x = –1/2xm, the kinetic and potential energies...
Homework Statement
A block attached to a spring oscillates in simple harmonic motion along the x axis. The limits of its motion are x = 10 cm and x = 50 cm and it goes from one of these extremes to the other in 0.25 s. Its amplitude and frequency are:
A) 40 cm, 2 Hz
B) 20 cm, 4 Hz
C) 40...
Homework Statement
A uniform rod of mass m and length 2L is bent into 2 straight segments about its
midpoint. The angle between the 2 segments is α. The bent rod is balanced on a sharp
fulcrum. Find the angular frequency for small oscillations if the rod is displaced from
equilibrium and...
Homework Statement
A vibrating strutural beam in a spacecraft can cause problems if the frequency of vibration is fairly high. Even if the amplitude of vibration is only a fraction of a millimeter, the acceleration can be several times greater than acceleration due to gravity. As an...
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A pendulum of length L with a bob of mass M hangs vertically. The bob is attached to a horizontal spring that has a force constant k. When the bob is directly below the pendulum support, the spring is unstretched. (a) Derive an expression for the period of the oscillating...
1. a. Jim and Gina are swinging on adjacent swings of equal length. Jim weighs about twice as much as Gina. Who takes less time to swing back and force.
I got this answer, which is that they take the same time since mass doesn't affect the period in simple harmonic motion. However, I don't get...
Homework Statement
A sim[le pendulum has a mass of .25kg and a length of 1.0m. It is displaced
through an angle of 15degrees and then released. What are (a) the maximum
speed, (b) the maximum angular acceleration, and (c) the maximum restoring
force? Solve the problem once by using the...
Homework Statement
A diving board oscillates with simple harmonic mothion of frequency 3.0 cycles per second.?
What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed there to not lose contact with the board during oscillation.
Homework...
Homework Statement
Write expressions for simple harmonic motion (a) with amplitude 10 cm, frequency 5.0 Hz, and maximum displacement at t=0; and (b) with amplitude 2.5 cm, angular frequency 5.0 1/s, and maximum velocity at t=0.Homework Equations
\begin{gathered}
x(t) = A\cos (\omega t +...
Simple Harmonic Motion- Spring problem
Homework Statement
A 12.5 kg mass is suspended on a 1e^5 N/m spring. The mass oscillates up and down from the equilibrium position
y(t)= Asin(wt+\phi)
Find the amplitude of the oscillating mass
Initial position- 4.9 cm
Initial velocity= +8.64...
The period of an oscillating particle is 56 s, and its amplitude is 18 cm. At t = 0, it is at its equilibrium position. Find the distances traveled during these intervals.
(a) t = 0 to t = 14 s
cm
(b) t = 14 s to t = 28 s
cm
(c) t = 0 to t = 7 s
cm
(d) t = 7 s to t = 14 s
cm
x =...
Hi everyone, this is my first post on this forum. I hope you can help and maybe one day I can help some of you ;)
Homework Statement
I need to determine the constants of pendulum. Θ ( in radians) and Φ.
I am given the length of the pendulum, 0.30m
and the initial angle of release, 0.10...
Homework Statement
A simple pendulum of mass m = .28 kg and length L = .65 m is attached to a cart of mass M = 1.0 kg. The mass of the pendulum support is negligible. The cart can roll rreely on a horizontal surface. At t = 0, the pendulum bob is released from rest when the string makes...
Homework Statement
A simple pendulum is made from a 0.653 m-long string and a small ball attached to its free end. The ball is pulled to one side through a small angle and then released from rest. After the ball is released, how much time elapses before it attains its greatest speed...
Homework Statement
A weight of mass m is placed on a string. as a result it exerts a force equal to xk that tends to reduce x, where k is the spring constand and x is the distance from the equilibrium position of the spring.
1. Confirm that x = Asin(wt+ f) is indeed a solution of...
Homework Statement
If you guys cannot read the problem due to all the latex not pasting properly I will post the link to the website.
http://courses.ncsu.edu/py411/lec/001/; then proceed to go to the homework section of my webpage then click on Assignment 6 and the problem is next to I...
Homework Statement
A particle of mass m moves in one dimension under the action of a force given by -kx where x is the displacement of the body at time t, and k is a positive constant. Using F=ma write down a differential equation for x, and verify that its solution is x=Acos(\omegat+\phi)...
Homework Statement
A certain oscillator satisfies the equation
x''+4x=0
x=\sqrt{3}
|x'|= 2
show that , in subsequent motion,
x=\sqrt{3} cos(2t)-sin(2t)
Deduce the amplitude of the oscillations. How long does it take for the particle reach its first origin?
Homework...
Homework Statement
A 150 grams particle oscillating in SHM travels 24 cm between the two extreme points in its motion with an average speed of 60cm/s
Find
a) angular frequency
b) the maximum force on the particle
C) the maximum speed
The Attempt at a Solution
My first...
I have a test soon and I don't get this topic!
Here are two questions I'm having trouble with:
1. A simple harmonic oscillator has total energy of E.
a) Determine the kinetic and potential energies when the displacement is (1/2)A. A = amplitude.
b) For what value of displacement does the...
Homework Statement
Low-frequency vertical oscillations are one possible cause of motion sickness, with 0.60hz having the strongest effect. Your boat is bobbing in place at just the right frequency to cause you the maximum discomfort.
Part A -
How much time elapses between two waves hitting...
A mass 0.2kg attached to the lower end of a light helical spring produces an extension of 0.05m.
Calculate the force constant of the spring.
The mass is pulled down a further 0.02m and released. Calculate the time period of subseuent oscillations and the maximum value of the accelartion...
Sand grains rest on a horzontal plate. The plate vibrates in the vertical plane with SHM of amplitude 1.5mm at a fixed frequency with acceleration equal to free fall (9.8ms^-2).
What will happen to the grains of sand when the frequency of vibration is increased?
I am unsure of how to tackle...
the conservation of energy formula for a dipole
\DeltaK=-\DeltaU
(1/2)Iw^2=-(-qEDcos(theta))
(1/2)Iw^2=qEDcos(theta)
E-field going parallel to the y-axis. if the positive end of the dipole was in the first quad with angle theta from the y-axis and the negative end of the dipole was in the third...
Homework Statement
A ring of radius 18 cm that lies in the yz plane carries positive charge 6x10^-6 C uniformly distributed over its length. A particle of mass m that carries a charge of -6 \muC oscillates about the center of the ring with an angular frequency of 29 rad/s.
Find the...
Equation given
u(t) =0.2 cos (wt) + 0.5 sin (wt), where w=3pi rad/s and displacement is in feet.
Describe the same motion using amplitute/phase format.
Describe the same motion using complex notation
For t =0.4 sec calculate u
How do you calculate u? and how do you describe the...
In graphs of SHM, it says that "identify and use relevant parameters from the following graphs"
1. displacement-time
My question is, what it meant by "relevant parameters"?