Damped Definition and 383 Threads

I have a damped linear oscillator, originally at rest in its equilibrium position [therefore, x(0)=0 and x'(0)=0]. It is subjected to a forcing function: F(t)/m = {0, if t<0 {a(t/tau), if 0<t<tau {a, if t>tau I have to find the response function. However, when I attempt to find the step...

what is the equation? i have something written down in my notes but i really don't get it... x=A(e^-kt)(cos omega t) first of all, how is the amplitude calculated if it decreases over time?? is it averaged? what is e? second of all, to calculate k, you need hooke's law and you need...

I'm having trouble with this problem.The suspension system of a 2100 kg automobile "sags" 7.2 cm when the chassis is placed on it. Also, the oscillation amplitude decreases by 35% each cycle. Estimate the values of (a) the spring constant k and (b) the damping constant b for the spring and shock...

Problem 1: I have a mathematical pendulum with a mass m connected to a string of length l. The pendulum is damped by air resistance that is proportional to the velocity, Ffric = -k*v. I need to derive the damping effect the air resistance has on the pendulum - that is, the decrease of the...

Problem 1: I have a mathematical pendulum with a mass m connected to a string of length l. The pendulum is damped by air resistance that is proportional to the velocity, Ffric = -k*v. I need to derive the damping effect the air resistance has on the pendulum - that is, the decrease of the...

I am really struggling with this question... Question: Consider a damped oscillator, with natural frequency w_0 (omega_0) and damping constant B (beta) both fixed, that is driven by a force F(t)= F_0*cos(wt). Find the rate P(t) at which F(t) does work and show that the average < P > over any...

Hello, On this page: http://galileo.phys.virginia.edu/classes/152.mf1i.spring02/Oscillations.htm It says (and shows) that in the case of a critically damped oscillation, it moves more quickly to zero than in the overdamped case. I don't understand why. The solution to this circuit is...

Here's the problem: A damped oscillator has a mass of .05 kg, a spring constant of 5 N/m, and a damping constant of .4 Ns/m. At t=0, the mass is moving at 3.0 m/s at x=.1m. Find x as a function of time. What I have done: I know the damping constant b = .4 and I have used this to find...

Please I don't understand this problem at all: Consider a driven damped harmonic oscillator.Calculate the power dissipated by the damping force? calculate the average power loss, using the fact that the average of (sin(wt+phi) )^2 over a cycle is one half? Please can I have some help for...

Sorry that I had to use an image file, I was having a lot of trouble using the Latex system. http://www.flamingice.5gigs.com/Question.gif Ok... We know the amplitude of the oscillations, and the force per person, so all we need to do is find Fmax, by finding other values and substituting...

Driven, damped harmonic oscillator -- need help with particular solution Consider a damped oscillator with Beta = w/4 driven by F=A1cos(wt)+A2cos(3wt). Find x(t). I know that x(t) is the solution to the system with the above drive force. I know that if an external driving force applied...

I'm having trouble with this problem. I want to get it into a form with cos but I'm stumped. The solution for damped simple harmonic motion is given by x = (e^(-rt/2m))(C_1*e^(iw't)+C_2*e^(-iwt)) If x = Acos phi at t = 0, find the values of C_1 and C_2 to show that x'=(approx)...

hi guys, doing damped and forced harmonic motion at college at the moment, but i don't do further maths...hence I'm a tad behind compared to those who do (half the class). we don't need to know it for the exam itself, but you know...curiosity. does anyone know of any good online resources...

Hi, I do not know how to drive an experession for energy loss of damped oscillator.I know that: X(t)=A exp(-Beta*t)cos(wt-delta) and: v=dx/dt... I found E=K+U but it seems to be so messy. It is like: E=(1/2)*m*(A^2)*exp(-2*beta*t)[ beta^2 (cos(wt-delta))^2)+beta* sin...

Can you help me start on this one: Show that an overdamped or critically damped oscillator can cross the origin at most once.

Question: (a) Show that the total mechanical energy of a lightly damped harmonic oscillator is E = E_0 e^{-bt/m} where E_0 is the total mechanical energy at t = 0. (b) Show that the fractional energy lost per period is \frac{\Delta E}{E} = \frac{2 \pi b}{m \omega_0} = \frac{2...

i am going to write a report about damped oscillation . as i planned , i will discuss the amplitude decays exponentially with time , application . but that are too little to talk to then what things need to be further discuss? and one question if i use one small card and bid card to damp...

I am confused! Forced oscillation is the one which a periodic force is imposed on a oscillating system. For a damped oscillator, the damping force is proportional to velocity which varies periodically. Does it mean that the damping force is a periodic force and the damped oscillation is a...

Question: A damped harmonic oscillator loses 5.0 percent of its mechanical energy per cycle. (a) By what percentage does its frequency differ from the natural frequency \omega_0 = \sqrt{k/m}? (b) After how may periods will the amplitude have decreased to 1/e of its original value? So, for...

A pendulum of length 1.00 m is released from an initial angle of 18.0°. After 500 s, its amplitude is reduced by friction to 5.5°. What is the value of b/2m? i have no idea how to do this prooblem, the book goes over this section really briefly... what the heck is b/2m?

Hi, I'm having a lot of trouble with a damped harmonic oscillator problem: A damped harmonic oscillator consists of a block (m=2.00kg), a spring (k=10 N/m), and a damping force (F=-bv). Initially it oscillates with an amplitude of 25.0cm. Because of the damping force, the amplitude falls...

i am finding damped SHM difficult to understand can anyone give sugestion as to what coul .do

hello all! i'm now on a project namely "physics & sports" and I'm to study the projectile motion of a basketball. the aim of my investigation is to find out the range of projection angle theta that allows the ball to get through the "loop" (actually, what's the name of the thingy?? well i mean...

a damped simple harmonic oscillator has mass m = 260 g, k = 95 N/m, and b = 75 g/s. Assume all other components have negligible mass. What is the ratio of the amplitude of the damped oscillations to the initial amplitude at the end of 20 cycles (Adamped / Ainitial)? having trouble getting...

I have two problems, the second of which I think I might be solving right. The web program we use to do our homework isn't accepting my answer. It might be the program's fault, but I'm not sure, so I'd like to check. Here's my first problem: Damping is negligible for a 0.131-kg object...

For a simple damped oscillator... \text {Apparently if } \beta \ll \omega_0 } \text { then ...} \omega_d \approx \omega_0[1-\frac {1}{2}(\beta/\omega_0)^2]} Given that: \beta=R_m/2m \text { (where } R_m= \text {mechanical resistance) } \text { and } \omega _d=\sqrt{(\omega...

Question: A damped harmonic oscillar loses 5.0 percent of its mechanical energy per cycle. (a) By what percentage does its frequency differ from the natural frequency \omega_0 = \sqrt{k/m}? (b) After how many periods will the amplitude have decreased to 1/e of its original value? (a) Let E(t)...

Hi I have two questions to ask and hopefully someone could help as I am getting little help from my college and work collegues 1) The work done by an air compressor is given by W = K [ (p1/p2)^(n-1/n) + (p1/p2)^(n-1/n)-2] where p1,p2,n and K are all constants. QUESTION - show that...

In my notes, there are two sentences make me feel strange... As we know, the pendulum whose length equals to that of the friver pendulum, its natural frequency of oscillation if the same of the frequency of the driving one. This is known as resonance oscillation. However, somewhere I found...

I am trying to calculate the force and velocity of a primary and secondary suspension. I know the damping constant of the dampers and the spring constant of the springs. I see where an expression can be calculated where you input time and get x.

Problem: A piece of wire of mass m and resistance R forms a circular ring of area A. It is suspended by an insulatd, massless rod of length l to form a frictionless pendulum in the presence of a uniform, vertical magnetic field B. The normal to the ring is parallel to its velocity. Find the...

Okie, doing homework for physics and I'm stuck. The section is on damped oscillations, question is as follows: A 10.6 kg object oscillates at end of a vertical spring that has a spring constant of 2.05 * 10^4 N/m. The effect of air resistance is represented by the damping coefficient b=3.00...

Hello people! I have quite a complex problem... I need to graph (on my PC, using excel or mathcad) the following motion: a cube on a spring with given k and given initial Energy oscilates on a horizontal surface with friction coefficient u. Now, i know this are damped oscillations which...