What is Simple harmonic motion: Definition and 913 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.
Hi everyone new here and hope i have put this in the right place?
If anyone could help me with this question i would be very grateful.
The value w(angular frequancy) is introduced into the analysis of simple harmonic motion
A) Because the unit of hz is not a convenient unit for frequancy
B)...
Homework Statement
A body of uniform cross-sectional area A and mass density ρ floats in a liquid
of density ρ0 (where ρ < ρ0), and at equilibrium displaces a volume V.
Making use of Archimedes principle (that the buoyancy force acting on a
partially submerged body is equal to the mass of the...
Homework Statement
"A small body rests on a horizontal diaphragm of a loudspeaker which is
supplied with an alternating current of constant amplitude but variable frequency.
If the diaphragm executes simple harmonic oscillation in the vertical
direction of amplitude 10 µm, at all frequencies...
Problem:
A 2.4-kg object on a frictionless horizontal surface is attached to one end of a horizontal spring of force constant k=4.5 kN/m. The other end of the spring is held stationary. The spring is strecthed 10 cm from equilibrium and released. find the system's total mechanical energy...
Homework Statement
"Two light springs have spring constants k1 and k2, respectively, and are used
in a vertical orientation to support an object of mass m. Show that the angular
frequency of small amplitude oscillations about the equilibrium state is
[(k1 + k2)/m]^1/2 if the springs are...
Homework Statement
a ball that has been placed on top of a coil spring with a spring constant of 575 N/m and a length (h1) of 25.0 cm. As the ball compresses the spring, it contacts a second spring that has a spring constant of 325 N/m and a length (h2) of 15.0 cm. If the ball is 12.5 cm...
Hi! Could someone please check if my following problems are correct? Any insight on why a problem is incorrect would be appreciated. Thanks!
1) An object is hung from a light vertical helical spring that subsequently stretches 2.0 cm. The body is then displaced and set in SHM. Compute the...
Homework Statement
A 0.26 kg mass attached to a spring undergoes simple harmonic motion with a period of 0.84 s. What is the force constant of the spring?
Homework Equations
T = 2*pi*SQRT(m/k)
The Attempt at a Solution
I know this is supposed to be an easy question, but for some...
Homework Statement
A 0.01 kg bullet is fired horizontally into a 2.50 kg wooden block attached to one end of a massless, horizontal spring (spring constant = 845 N/m). The other end of the spring is fixed in place, and the spring is unstrained initially. The block rests on a horizontal...
F_s=-kx=ma, a=\frac{-kx}{m}
We now need to find an equation that satisfies: \frac{d^2x}{d^2t}=\frac{kx}{m}
We get (letting w^2=k/m): x(t)=A*Cos(wt+\phi)
The time it takes for one cycle is:T_1=2 \pi\sqrt{\frac{m}{k}
Now, let's solve for T again using a different method...
simple harmonic motion --> amplitude independent of mass?
I know that acceleration is directly proportional to displacement, but opposite in sign, and that acceleration and displacement are related by the square of the frequency. But i was wondering if amplitude is independent of mass in...
I'm going to dispense with the provided template for this, I hope no one minds.
I always understood that for simple harmonic motion there was this equation:
\omega = \sqrt{\frac{k}{m}}
However, I recently got a book that helps you study for the Physics GRE (Graduate Record Examination).
There...
Homework Statement
A spring, of negligible mass and which obeys Hooke's Law, supports a mass M on an incline which has negligible friction. The figure below shows the system with mass M in its equilibrium position. The spring is attached to a fixed support at P. The spring in its relaxed state...
Homework Statement
A person who weighs 665 N steps onto a spring scale in the bathroom, and the spring compresses by 0.67 cm.
(a) What is the spring constant?
(b) What is the weight of another person who compresses the spring by 0.37 cm?
Homework Equations
f=-Kx...
Homework Statement
An object is undergoing simple harmonic motion with period 0.280 s and amplitude 5.95 cm . At t=0 the object is instantaneously at rest at x= 5.95 cm.
Calculate the time it takes the object to go from x= 5.95 to x= -1.44 .
Homework Equations
X=A.cos(wt) ------> the...
Homework Statement
A spring is hung from the ceiling. A 0.450-kg block is then attached to the free end of the spring. When released from rest, the block drops 0.150 m before momentarily coming to rest. (a) What is the spring constant of the spring? (b) Find the angular frequency of the...
A 28.0 kg block at rest on a horizontal frictionless air track is connected to the wall via a spring. The equilibrium position of the mass is defined to be at x=0. Somebody pushes the mass to the position x= 0.350 m, then let's go. The mass undergoes simple harmonic motion with a period of 4.70...
Homework Statement
The velocity of an object in simple harmonic motion is given by v(t)= -(0.269 m/s)sin(15.0t + 2.00π), where t is in seconds. What is the first time after t=0.00 s at which the velocity is -0.150 m/s?
Homework Equations
already given in question
The Attempt at a...
Homework Statement
If a particle undergoes SHM with amplitude 0.18 m, what is the total distance it travels in one period?
Homework Equations
The Attempt at a Solution
My physics teacher did not explain any of this to us, and I just don't know where to start!
Homework Statement
A mass of 10g is suspended from a spring of unstreched length 80cm. The extension produced is 1cm. The mass is pulled down a further 0.5cm and then released. Find:
a) the period of motion
b)the maximum speed of the mass
c) the max Ke of the mass
d)the tension in the...
Homework Statement
While visiting friends at Cal State Chico, you pay a visit to the Crazy Horse Saloon. This fine establishment features a 200- kg mechanical bucking bull that has a mechanism that makes it move vertically in simple harmonic motion. Whether the “bull” has a rider or not, it...
I've been going through and proving to myself that the solution to the SHM equation is correct; at A level we were just told what it was but never really shown why.
I've gone through the problem as a standard 2nd Order ODE (with complex roots of course) and ended up at:
x = A_{real}...
Homework Statement
What will be better to take to the moon, a spring clock or a pendulum clock. Why?
Homework Equations
F= -k*(Delta)x
k = g m/Dx
T = 2*π*[square-root of:(m/k)]
The Attempt at a Solution
I know that there is less gravitational force while on the moon...
1.
A spring with spring constant 14.5 n/m hangs from the ceiling.
A 430g ball is attached to the spring and allowed to come to rest.
It is then pulled down 7.20cm and released.
What is the time constant if the ball's amplitude has decreased to 3.70 after 52.0 oscillations?
The...
Homework Statement
A cylindrical wooden log is loaded with lead at one end so that it floats upright in water. The length of the submerged portion is L = 2.56m. The log is set into vertical oscillation.
(a) Show that the oscillation is simple harmonic
(b) Find the period of oscillation...
When a string, fixed at both ends, has a force exerted on it, how do you determine what the amplitude will be, if the tension, applied force, and length are known?
Homework Statement
1. Do you use the equation of continuity and Bernoulli's equation simultaneously in a question? When do you use them?
2. In simple harmonic motion, why is the velocity shifted to left of the displacement by pi/4?
Homework Equations
pressure + .5density x velocity...
Homework Statement
Using experimental values for mass and period of oscillations, I'm trying to graph period^{2} (y-axis) against mass (x-axis) to get a gradient = 4(pi^{2})/k so I can find k (spring constant).
The problem is that when I use each pair of results in the equation below, I...
I have this right or wrong question in physics that i know the answer to but not the way to solve it can you help me with it?:
2 identical springs were put Vertically. if one was pulled 5cm (spring1) and the other was pulled 10cm(spring2) and were left to move a simple harmonic motion would...
Homework Statement
An oscillator consists of a block attached to a spring (k = 125 N/m). At some time t, the position (measured from the system's equilibrium location), velocity, and acceleration of the block are x = 0.800 m, v = -11.3 m/s, and a = -119 m/s2
(a) calculate the frequency of...
Homework Statement
A mass on a spring undergoes simple harmonic motion with amplitude A.
a) In a time equal to three periods, what is the magnitude of the displacement of the mass?
b) In a time equal to three periods, what actual distance did it travel?
Homework Equations
The...
In physics class, we had to do a lab where a mass was attached vertically to a spring system. The spring went through simple harmonic motion. We stretched the mass and let go of it. We then used a software to determine the kinetic energy, the elastic potential energy, and the total energy. We...
Homework Statement
If the slope of your gradient turns out to be 4.041 s^2.m^-1 then what value would you obtain for g? State your answer in m.s^2 and to 3 significant figures.
Homework Equations
T^2 = (4 pi^2 e1 / g) - (4 pi^2 e0 / g)
This is the one I'm supposed to use. Other ones...
Homework Statement
A mass "m" is attached to the free end of a light vertical spring (unstretched length L) of spring contant "k" and suspended from a ceiling. The spring streches by Delta L under the load and comes to equilibrium at a height "h" above the ground level (y=0). The mass is...
Homework Statement
2 equal masses are joined together by a spring of stiffness k. each of the masses is then connected to a wall with an identical spring. derive the equations of motion in matrix form. (a diagam has 2 masses with x1 on top of the first mass and x2 on top of the second.)...
Homework Statement
A 50 g mass hanger hangs moitionless from a partially stretched spring. When a 91 gram mass is added to the hanger, the spring stretch increases by 7 cm. What is the spring constant of the spring (in N/m)? (Assume g = 9.79 m/s2.)
Homework Equations
F=k(delta)L-mg...
Homework Statement
what is the form of the equation of motion for the SHM of a mass suspended on a spring when the mass is initially (a)released 10 cm above the equilibrium position; (b) given an upward push from the equilibrium position, so that it undergoes a maximum displacement of 8cm; (c)...
i just studied S.H.M and i am wondering is the displacement equals the amplitude or zero after the periodic time?
because when i thought it equals zero at first because the periodic time is time required for the object to make acomplete oscillation and return to it's starting point right?
but...
Homework Statement
The pendulum of a clock is replaced by a spring-mass system with the spring having spring constant 0.1 N/m. What mass should be attached to the spring?
Homework Equations
T=2 pi (m/k)1/2
The Attempt at a Solution
1 = 2 pi (m/0.1)1/2
1 = 4 pi2 m/0.1...
Homework Statement
A body oscillates with simple harmonic motion along the x-axis. Its displacement varies with time according to the equation x = 5 sin(πt + π/3) meters. The acceleration in m/s2 of the body at t = 1 second is approximately
Homework Equations
The harmonic motion ones I...
Homework Statement
A mass M is connected between 2 stretched springs, as shown. The equilibrium length of each spring is L, they are stretched to twice this length when m is in equilibrium. Consider the oscillations in the + and - x direction as shown in the figure...
Homework Statement
The figure below shows the x(t) curves for three experiments involving a particular spring-box system oscillating in SHM.
(a) Rank the curves according to the system's angular frequency, greatest first (use only the symbols > or =, for example 1>2=3).
(b) Rank the curves...
The equation of simple harmonic motion is given as
(d2x)/(dt2)+xk^2=0
Could someone show me HOW we arrive at the general solution to this second order ODE
Hello
I'm trying to find a formula for a Simple Harmonic Oscillator.
After some algebra I've got it down to;
\ddot{r}-A*\sqrt{r^{2}-B^{2} } = 0
where A and B are constants.
I'm trying to get it down to be in the form of
\ddot{r} + C*r = 0
I am feeling like a dummy cause it...
Homework Statement
A 3.2-kg block is hanging stationary from the end of a vertical spring that is attached to the ceiling. The elastic potential energy of this spring/mass system is 1.8J. What is the elastic potential energy of the system when the 3.2-kg block is replaced by a 5.0-kg block...
Thank you in advance!
Homework Statement
A 3.0-kg block is between two horizontal springs. Neither spring is trained when the block is at the position labeled x=0 m in the drawing. The block is then displaced a distance of 0.070m from the position where x=0m and is released from rest. (a) What...
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...
Homework Statement
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...
Homework Statement
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...