Harmonic motion Definition and 1000 Threads

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...

is the rotation of the Earth and the revolution of it around sun simple harmonic in nature? it is periodic but not linear.

A new car, car 1, has a spring-loaded rear bumpe with a force constant of 8.4 x 10^5 N/m. While car 1 is parked, a second vehicle, car 2 (with a mass of 1.5 x 10^3 kg), travels at a constant speed of 18 km/h (5 m/s), hitting car 1 in the rear bumper. a) Calculate the kinetic energy of car 2...

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...

http://img13.imageshack.us/img13/9091/53337497.th.jpg Can someone please help me with the problem above? I am unable to start it. Clearly, using the constant acceleration "suvat" equations, 0.5ft^2 is the distance obtainined, however I am unable to proceed. Thanks in advance.

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...

The position x(t) of a mass undergoing damped harmonic motion at an angular frequency ω' is described by x(t)=A e^t/τ cos(ώt + delta) where τ is the time constant, A the initial amplitude and delta an arbitrary phase. (a) Find an expression for the speed of the mass as it...

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 1. The St. Louis Arch has a height of 192m. Suppose a stunt woman of mass 60kg jumps off the top of the arch with an elastic band attached to her feet. She reaches the ground at zero speed. Find her kinetic energy K after 2 sec of the flight. Assume that the elastic band...

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...

I am attempting to derive the equation for dampened harmonic motion from the differential equation: m\frac{d^2 x}{dt^2}+b\frac{dx}{dt}+kx=0 It would be painful to type the whole derivation out, but there is one point relevant to the problem I am having. In order to get SHM, we assume that...

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...

Homework Statement Consider a particle in the harmonic potential V(x)= \frac{m\omega^2 x^2}{2} . Its lowest energy eigenvalue is E_0=\hbar \omega/2 and the eigenfunction associated with this energy, ie the ground-state wave function, is \phi_0(x) = \left(\frac{m\omega}{\pi...

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...