Simple harmonic motion Definition and 917 Threads

Homework Statement A small sphere with mass m is attached to a massless rod of length L that is pivoted at the top, forming a simple pendulum. The pendulum is pulled to one side so that the rod is at an angle θ from the vertical, and released from rest. When the pendulum rod is...

Hi I am trying to model SHM in Simulink as shown here: http://pundit.pratt.duke.edu/wiki/Simulink/Tutorials/DiffEq I have tried using different values of spring constant and damping to get instant response to the input force. I am measuring the displacement calculated by SHM. The force changes...

Homework Statement A mass oscillates along the x-axis in simple harmonic motion. It goes through 200 cycles in 10 seconds and its vibrational amplitude is 0.020 m. What is the frequency, in hertz, and the total distance traveled, in meters, by the mass in the 200 cycles? Homework...

Homework Statement A particle is in simple harmonic motion with period T and with position as a function of time given by x(t) = A cos(wt+ø). At time t = 0 the particle is at x = A/2 with positive velocity. The next time it is at the same position is ___? Homework Equations...

Homework Statement A mass of 0.4 kg, hanging from a spring (k= 80N/m) is set into an up-and-down SHM. What is the speed of the mass when moving through the equilibrium point? The starting displacement, A, is 0.10 m. Homework Equations a = -kx/m ω = 2pi/TThe Attempt at a Solution I tried to...

Homework Statement The function x = (7.4 m) cos[(5πrad/s)t + π/5 rad] gives the simple harmonic motion of a body. At t = 6.2 s, what are the (a) displacement, (b) velocity, (c) acceleration, and (d) phase of the motion? Also, what are the (e) frequency and (f) period of the motion...

Problem: Show that the combined spring energy and gravitational energy for a mass m hanging from a light spring of force constant k can be expressed as 1/2 ky2, where y is the distance above or below the equilibrium position. Figure shows a block connected to spring, where equilibrium is...

Homework Statement I was wanting to get some clarification on some of the simple harmonic motion equations. So, say for example there is a box of mass "m" undergoing simple harmonic motion attached to a spring of spring constant K on a horizontal surface. To find where the box is, as a...

Homework Statement a small object is mounted to the perimeter of a hoop of radius r. The mass of the object and the hoop is the same. The hoop is placed into a fixed semi-cylinder shaped rough trough of radius R, such that the small mass is at the top. Find the least R/r ratio such that the...

The nonlinear oscillator $y'' + f(y)=0$ is equivalent to the Simple harmonic motion: $y'= -z $, $z'= f(y)$ the modified Symplectic Euler equation are $$y'=-z+\frac {1}{2} hf(y)$$ $$y'=f(y)+\frac {1}{2} hf_y z$$ and deduce that the coresponding approximate solution lie on the family of curves...

Homework Statement An object moving with harmonic motion has an acceleration of -2 m/s^2 when the elongation is 0.5 m. Determine the angular frequency and the velocity and acceleration for t=1s. Homework Equations a=-ω2x (1) x=Acos(ωt+θ) (2) a=-Aω2cos(ωt+θ) (3) The Attempt at a...

Hi I am using Simple Harmonic Motion in a Matlab/Simulink model. Instead of using a motion for a simple pendulum, I decided to use a spring with a mass. The reasons for this is because my example is more like a lever attached to a pivot point and having an object at the end with a mass. A...

Homework Statement Hi, so my question is about a damped simple harmonic motion experiment The experiment is as follows: A 30 cm ruler with a needle attached to it is clamped to a bulldog clamp. The needle is placed in a beaker of water so that it is just inside the water ( by about...

The problem is a ball is dropped onto a spring and the spring compresses .95m. The ball then sticks to the spring and oscillates with a period of 1.1 seconds and has a mass of 6kg. I thought that the equation mg(h+x)=1/2(k)(x^2) would be what i would use. I got h=.47m I also...

Homework Statement Write a simple harmonic motion with amplitude 14cm , frequency 3.0Hz , and maximum displacement at t=0.The Attempt at a Solutiony (t) = A cos (ωt) = 14 cos (2πt/T) Dealing with angular frequency is easy. But deal with natural frequency throws me off course.

1. What is the difference between ψ = Amod(t) cos (wavt)and the simple harmonic oscillator? 3. A. The amplitude is time dependent B. The amplitude,Amod , is twice the amplitude of the simple harmonic oscillator, A. C. The oscillatory behavior is a function of ? instead of the period, T...

Homework Statement An object is undergoing simple harmonic motion with frequency f = 3.1 Hz and an amplitude of 0.15 m. At t = 0.00 s the object is at x = 0.00 m. How long does it take the object to go from x = 0.00 m to x = 7.00×10-2 m. Homework Equations x(t)=Asin(ωt) The Attempt...

If we apply the small angle approximation so that a simple pendulum can be considered to be under going SHM, what kind of potential energy would the pendulum bob be having? If the answer is gravitational potential energy, then we have a contradiction because this would mean that the bob would...

For a mass on a spring (vertical set up) why is potential energy U defined as 1/2 kx^2? This is just the elastic potential energy. Shouldn't it be U = 1/2 kx^2 + mgh? Both the elastic AND potential energy? Also, for a simple pendulum at a very low amplitude, the potential energy is all...

For a mass on a spring (vertical set up) undergoing SHM, we equate the restoring force, -kx, to -ω^2 x, coming to a conclusion that ω = \sqrt{\frac{k}{m}}. My question is, is the restoring force |mg - T| Where T is the tension in the spring? Because this seems to be the net force. I am used to...

Simple harmonic motion (Again) :( This is not a question about a problem it is more about the position of a simple harmonic oscillator as a function of time:) I went through it in a lecture yesterday and found using the energy in simple harmonic motion to bex(t)= A cos(ωt +φ) Which is fine...

I have a question about the derivation that I have attached! I understand that both KE and U are 1/2 kA^2 So how is it that the two combine is also equal to 1/2kA^2Not sure if I'm missing something but I'm a little confused :(

Homework Statement Find the period of low-amplitude vertical vibrations of the system shown. The mass of the block is m. The pulley hangs from the ceiling on a spring with a force constant k. The block hangs from an ideal string...

What is a good way to memorize that ## \omega = \sqrt{\dfrac{k}{m}} ## ? I always confuse it with: ## T = 2\pi \sqrt{\dfrac{m}{k}}## , and can never tell them apart. (i guess part of it is that I'm not too familiar with it yet)

Homework Statement A 1.15-kg mass oscillates according to the equation x = .650cos(8.40t) where x is in meters and t in seconds. Determine a)the amplitude, b)the frequency, c) the total energy of the system, and d) the kinetic and potential energy when x = 0.360m. Homework Equations x...

I have doubts of how can I put my frame of reference in a simple harmonic motion vertical spring. Normally the books choose the origin in the equilibrium position and the positive distance (x>0) downward, and in this conditions Newton´s second law is: ma=-kx; but instead of putting the positive...

I need help for the second part please. How do the oscillations being damped prevent them from being S.H.M. as well the other 2 points? I need an explanation so I can understand. The oscillations would still have the same time period eve if they are damped. Low frequency due to...

Homework Statement The masses in figure slide on a frictionless table.m1 ,but not m2 ,is fastened to the spring.If now m1 and m2 are pushed to the left,so that the spring is compressed a distance d,what will be the amplitude of the oscillation of m1 after the spring system is released...

Homework Statement ) Two uniform, solid cylinders of radius R and total mass M are connected along their common axis by a short, massless rod. They are attached to a spring with force constant k using a frictionless ring around the axle. If the spring is pulled out and released, the cylinders...

Homework Statement Two points, each of charge Q, are fixed at either end of a frictionless rod of length 2R. Another point charge, of charge q (not Q) is free to move along the rod. Show that if charge q is displaced a small distance x (0<x<<R) from the centre of the rod, it will undergo...

I am a little confused with this subject. If you have a mass hanging from a spring, there is a specific equilibrium point, but what if you apply a force downwards on the mass, will this have an effect on the equilibrium position or will it remain the same? thanks!

Homework Statement So with pendulums in SHM, in my A level physics textbook (AQA Physics A), it shows a pendulum that has been displaced from equilibrium. It says that the restoring force is provided by the object's weight. Why isn't the restoring force provided by the tension in the string...

Well I was going through class lecture notes and my professor wrote this When x = A(the maximum value), v=0: E=1/2kA^2 When v = wA, x=0: E=1/2mw^2A^2 where w = omega, A = amplitude, k = spring constant, m = mass, v = velocity and apparently both equations are equal, i would like to...

Homework Statement if a pendulum has a period of .36s on Earth, what would its period be on the moon Homework Equations T=2pi sqrt l/g The Attempt at a Solution How do u go about solving thAt without length?

Homework Statement Mass = 2.4 kg spring constant = 400 N/m equilbrium length = 1.5 The two ends of the spring are fixed at point A, and at point B which is 1.9m away from A. The 2.4 kg mass is attached to the midpoint of the spring, the mass is slightly disturbed. What is the period of...

Homework Statement Two pendula of length 1.00m are set in motion at the same time. One pendula has a bob of mass 0.050kg and the other has a mass of 0.100kg. 1. What is the ratio of the periods of oscillation? 2. What is the period of oscillation if the initial angular displacement is...

Homework Statement Two-dimensional SHM: A particle undergoes simple harmonic motion in both the x and y directions simultaneously. Its x and y coordinates are given by x = asin(ωt) y = bcos(ωt) Show that the quantity x\dot{y}-y\dot{x} is also constant along the ellipse, where here the...

So over the weekend my physics prof has assigned an assignment where one of the questions is as follows and here is my thought process: A massless spring hangs from the ceiling with a small object attached to its lower end. The object is initially held at rest in a position yi such that the...

Hello, I was being taught AC in High School, It was good but the way they taught us DC, things like drift velocity, no of electrons per unit volume etc, it was easy to visualize electrons rushing in a conductor. I tried to visualise AC(which was not taught to us) and I came to a conclusion...

Homework Statement Derive the equilibrium state of a simple harmonic oscillation and show that the derivative of the maximum displacement is s^{'} = 2 \sqrt{E} Homework Equations F = -k x The Attempt at a Solution m a = -k s \rightarrow ms^{''}...

Homework Statement A spring is freely hanged on a ceiling. You attach a mass to the end of the spring and let the mass go. It falls down a distance of 49 cm and comes back to where it started. It contineous to oscillate in a simple harmonic motion going up and down - a total distance of 49...

Hello, When doing problems with SHM, my textbook says something like: An object in vertical shm is described by <insert some function>. Find the speed after X seconds. my question is, how do you know if the function is referring to the position of the object, or the velocity, or...

Homework Statement A simple pendulum is 5m long. What is the period of the oscillations for this pendulum in an elevator accelerating upwards at 5m/s2 and accelerating downards at 5m/s2Homework Equations ω = √(g/L) T = 2∏ / ωThe Attempt at a Solution I got the right answers (trial and...

Homework Statement The displacement of a particle along x-axis given by x=A sin^2(wt), where the symbols have their usual meaning. Is the particle motion simple harmonic? also find its time period. Homework Equations simple harmonic eqn iss of the form x=Asin(wt) or x=acos(wt)...

Hello why we use cosine and sine in simple harmonic motion? why we use particularly cosine with potential energy and sine with kinetic energy of simple harmonic oscillator? regards

Homework Statement A uniform meter stick of mass M is pivoted on a hinge at one end and held horizontal by a spring with spring constant k attached at the other end. If the stick oscillates up and down slightly, what is its frequency? Homework Equations τ=rFsinθ f=(1/2π)√(k/m) F=kx...

Homework Statement A mass hanging from a spring is displaced and released so that it vibrates vertically. Its maximum height above a tabletop is 30 cm and its minimum height above the table top is 12 cm. The mass vibrates 20 times per minute. At time 0, its height is 30 cm...

Homework Statement A particle with a mass of 65 g is moving with simple harmonic motion. At time t = 0, the particle is at its extreme positive displacement of 18.0 cm. The period of the motion is 0.600 s. Find the vecocity of the particle at t = 1.35 s Homework Equations (1). ω=2∏/T...

Question--- Angular Simple Harmonic motion.. Homework Statement A spherical ball of mass "m" and radius "r" rolls without slipping on a rough concave surface of large radius "R". It makes small oscillations about the lowest point. Find the time period of such oscillations. Homework...

Homework Statement A 0.241-kg particle undergoes simple harmonic motion along the horizontal x-axis between the points x1 = -0.349 m and x2 = 0.419 m. The period of oscillation is 0.511 s. Find the frequency, f, the equilibrium position, xeq, the amplitude, A. Homework Equations The...