Damped Definition and 383 Threads

Homework Statement A damped oscillator is subjected to a simple harmonic force, satisfying $$\ddot{x}(t) + 2k\dot{x}(t) + \omega^2x(t) = g \cos (nt), $$where ##g, k, \omega, n +ve.## 1) Show that for ##t >>1/k## the position x(t) has the form ##A \cos (nt - \phi)##, and find A and ##\phi##...

$$ -\sum_{n = 0}^{\infty}n^2\omega^2C_ne^{in\omega t} + 2\beta\sum_{n = 0}^{\infty}in\omega C_ne^{in\omega t} + \omega_0^2\sum_{n = 0}^{\infty}C_ne^{in\omega t} = \sum_{n = 0}^{\infty}f_ne^{in\omega t} $$ How can I justify removing the summations and solving for $C_n$? $$...

Homework Statement I have a ball of 20 kg describing a damped harmonic movement, ie, m*∂^2(x)+R*∂x+K*x=0, with m=mass, R=resistance, K=spring constant. The initial position is x(0)=1, the initial velocity is v(0)=0. Knowing that v(1)=0.5, v(2)=0.3, I have to calculate K and R...

This is not really a homework problem but rather a question about an equation for displacement in damped harmonic oscillations that I've come across during revision for midterms. In my notes and in various textbooks the equation is given as x=C\mathrm{exp}(-\frac{b}{2m}t)\cdot\mathrm{exp}(\pm...

I am investigating the mathematics behind driven damped oscillators, I will then simulate it in MATLAB and observe the unpredictable long term behavior of the system. In order to create non-linearity in a oscillating spring I can no longer use hookes law but a form of it by introducing a...

Homework Statement I have a mass, B, attached to a vibrating wall. The wall is vibrating at two frequencies, .01 Hz and 75 Hz (later in the problem it turns out that we want to transmit the .01 Hz but not the 75 Hz oscillations). The spring constant is k=154 N/m, the mass of the block B is 54.7...

I was reading Strogatz's book on nonlinear dynamics and chaos and in Example 7.2.2, he stated the energy function of the nonlinear oscillator \ddot{x} + (\dot{x})^3 + x = 0 as E(x, \dot{x}) = \frac{1}{2} (x^2 + \dot{x}^2) But isn't this the energy function for the harmonic...

the damped oscillator equation: (m)y''(t) + (v)y'(t) +(k)y(t)=0 Show that the energy of the system given by E=(1/2)mx'² + (1/2)kx² satisfies: dE/dt = -mvx' i have gone through this several time simply differentiating the expression for E wrt and i end up with dE/dt =...

the damped oscillator equation: (m)y''(t) + (v)y'(t) +(k)y(t)=0 Show that the energy of the system given by E=(1/2)mx'² + (1/2)kx² satisfies: dE/dt = -mvx' i have gone through this several time simply differentiating the expression for E wrt and i end up with dE/dt =...

1. What is the angular frequency of a damped oscillator whose spring stiffness is 15 cm with a 19.6 N mass and a damping constant of 15 kg/s? 2. ω0 = √(k/m) ----where k = spring constant and m=mass ζ= c/(2√(mk)) -----where m = mass, k = spring constant, and c = damping constant...

In the figure below, a damped simple harmonic oscillator has mass m = 300 g, k = 95 N/m, and b = 70 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)? I...

$$ u_{tt} + 3u_t = u_{xx} $$ $$ u(0,t) = u(\pi,t) = 0 $$ $$ u(x,0) = 0\quad\text{and}\quad u_t(x,0) = 10. $$ \begin{alignat*}{3} u(x,t) & = & \exp\left[-\frac{3t}{2}\right]\sin x\left[A_1\cosh\frac{t\sqrt{5}}{2} + B_1\sinh\frac{t\sqrt{5}}{2}\right]\\ & + &...

$$ u_{tt} + 3u_t = u_{xx}\Rightarrow \varphi\psi'' + 3\varphi\psi' = \varphi''\psi. $$ $$ u(0,t) = u(\pi,t) = 0 $$ $$ u(x,0) = 0\quad\text{and}\quad u_t(x,0) = 10 $$ \[\varphi(x) = A\cos kx + B\sin kx\\\] \begin{alignat*}{3} \psi(t) & = & C\exp\left(-\frac{3t}{2}\right)\exp\left[t\frac{\sqrt{9...

hey, could you help me with a few examples of Underdamped and Over damped systems?

Homework Statement Hello, I've recently finished an experiment on forced damped simple harmonic motion with a CLR "capacitor , inductor, resistor" circuit with the aim to measure the resonance frequency of the system, using a family of graphs for which each the resistance is varied. voltages...

Hi! The damped oscillator equation is as follows: x(t)= A exp(γt/2) cos(ωt) where ω= √( (w0)^2 + (γ^2)/4 ) I have attached a graph of a damped oscillator. The question is if I use graph to measure angular frequency, will it be w0 or ω? It should be w0 because if I put γ=0, I should...

Can someone derive for me the equation ωd=ωnsqrt(1-ζ2) Thanks

Homework Statement The displacement amplitude of a lightly damped oscillator with m=0.250kg and k=6400N/m is observed to decrease by 15% in exactly five minutes a) Calculate the fraction (in%0 of the initial mechanical energy of the oscillator that has been converted to other forms of energy...

d2x + 2Kdx + w0 2 x(t) = 0 dt dt while solving this we assume the solution to be of form x = f(t)e-kt why is this exponential taken?

Just have a few questions regarding the method of solving the damped-driven harmonic oscillator. Once we have rewritten the differential equation in terms of z and it's derivatives, we try a solution z(t) = Ce^{i \omega t}. When we sub in z and it's derivatives we then rewrite the complex...

Homework Statement Does the time for one oscillation, change during the damped oscillations? and please explain Homework Equations The Attempt at a Solution

Homework Statement http://img534.imageshack.us/img534/6503/questiono.jpg Homework Equations The Attempt at a Solution (a) I'm not sure how to approach this part. I appreciate any help to get me started. (b) I know that the period of oscillation is given by T'=\frac{2 \pi}{\omega '} I...

Homework Statement A damped harmonic oscillator loses 6.0% of it's mechanical energy per cycle. (a) By what percentage does it's frequency differ from the natural frequency f_{0} = (\frac{1}{2\pi})\sqrt{\frac{k}{m}}? (b) After how many periods will the amplitude have decreased to...

A proportionally damped 2-DOF system has mass and stiffness matrix M and K. We also know that the system has damping ratio ζ1 = 0.1 and 2 = 0.3. The damping matrix is written as C = α M + β K + γ KM-1K Try to find the coefficients Mx"+Cx'+kx=0 CM^-1K=KM^-1C...

Something i am doing is not adding up. I don't understand the part with the external force. here's the question: Show that the solution for the damped free forced vibration given by is when , where something along the way I'm doing wrong, because not for heck can i get that fraction with...

Homework Statement Find the steady-state solution having the form https://webwork3.math.ucsb.edu/webwork2_files/tmp/equations/e1/348e8eb8a4ddf62dd06b46276196e71.png for the damped system x'' + x' + x = 2cos(3t) Homework Equations Acos3t + bsin3t The Attempt at a Solution To be...

So the equation is x'' + 10x' + 64x = 0 x(0) = 1 x'(0) = 0 I get general solution of e^(-5t)(c1*cos(6.245t) + c2sin(6.245t) ) From there I get e^(-5t)cos(6.245t)+5e^(-5t)sin(6.245t) but it wrong. What the gerbils am I doing wrong? Thanks

If the damping ratio of a damped circuit is increased, does the circuit become more or less damped? I would think it would become more damped, but what exactly is the definition of the damping ratio?

Homework Statement A damped mass-spring system oscillates at 263 Hz. The time constant of the system is 7.4 s. At t = 0 the amplitude of oscillation is 3.4 cm and the energy of the oscillating system is 11 J. What is the amplitude of oscillation at t = 6.7 s? How much energy is...

Homework Statement Consider a damped oscillator, with natural frequency ω_naut and damping constant both fixed, that is driven by a force F(t)=F_naut*cos(ωt). a) Find the rate P(t) at which F(t) does work and show that the average (P)avg over any number of complete cycles is mβω2A2. b)...

Homework Statement Sinusoidal driving force driving a damped oscillator (mass = m). Natural frequency is assumed to equal the drive frequency = w Time has elapsed to the point any transients have dissipated. Show that the energy dissipated by the damping force [F=-bv] during one cycle is...

Homework Statement I need to develop an equation for the damping factor with respect to time for a pendulum that consists of a spherical mass attached to a string that is damped by air resistance. Homework Equations We are given that the curve fit for the drag coefficient is...

Homework Statement 3. A damped oscillator's amplitude dec¡eases from 8 cm to 4 cm in 20 seconds, If the intial energy of the oscillator is 64 J, what is the energy âfter 40 seconds? (Recall: E: (l/2)kA2) Homework Equations not sure how to approach the problem The Attempt at a...

Homework Statement Given damping constant b, mass m spring constant k, in a damped driven oscillation system the average power introduced into the system equals the average power drained out of the system by the damping force, for what values of ω does the instantanious damping power =...

Homework Statement http://desmond.imageshack.us/Himg812/scaled.php?server=812&filename=quesq.jpg&res=medium Homework Equations F = ma, F = -kx, SHM equations The Attempt at a Solution Here's the diagram they've done for part (b)...

How can we tell whether a given v0 will cause an oscillator to overshoot the equilibrium? If the velocity high enough, we know the oscillator will overshoot and return to equilibrium. But if v0 is low, the system would act like it came from a point a bit farther out and not overshoot (right?)...

Homework Statement A mass of 1000 kg drops from a height of 10.0 m onto a platform of negligible mass. It is desired to design a spring and damper on which to mount the platform so that it will settle to a new equilibrium position 2.00 m below its original position as quickly as possible...

Homework Statement I was wondering if there was a general method for finding a function that fits a set of data for a damped harmonic oscillator I'm currently writing up a presentation on the experiment for the gravitational constant and the way i did the experiment was to use a torsion...

Homework Statement Problem: A 2.0 kg block oscillates up and down on a spring with spring constant 240 N/m. Its initial amplitude is 15 cm. If the time constant ("tau") for damping of the oscillation is 4.0 s, how much mechanical energy has been dissipated from the block-spring system after 12...

1. Homework Statement [/b] Consider the damped oscillator illustrated in the figure below. Assume that the mass is 365g, the spring constant is 112N/m, and b = 0.117kg/s. How long does it take for the amplitude to drop to half its initial value? (A*e-b*t/(2m))...

Hi All, This is my first post here, and thanks in advance for any help and direction. I'm trying to model an enclosed damped mass spring system with an external forcing function acting on the system (not on the mass directly). Ultimately I would like to plot/calculate the motion (y) of...

Homework Statement Undamped oscillator's period T_0 = 12s. Damped oscillator's angular frequency \omega_1 = \omega_0 * 97\% where \omega_0 is the angular frequency of the undamped oscillator's. What is the ratio of consecutive maximum amplitudes? Homework Equations Equation of damped...

I'm not sure I'm in the right forum but I'll try and ask anyways. So I simulated a damped, driven pendulum in Java with the goal of showing period doubling/chaotic behavior. But then, as I was increasing the driving force, i saw the double period born. Then the 4-period...but then suddenly...

A damped oscillator is described by the equation m(x'') + b(x') + kx = 0, where the damping force is given by F = -b(x'). Show that the rate of change of the total energy of the oscillator is equal to the (negative) rate at which the damping force dissipates energy.

Homework Statement A small cuckoo clock has a pendulum 25 cm long with a mass of 10 g and a period of 1 s. The clock is powered by a 200 g weight which falls 2 m between the daily windings. The amplitude of the swing is 0.2 rad. What is the Q (quality factor) of the clock? How long would the...

Homework Statement A small cuckoo clock has a pendulum 25 cm long with a mass of 10 g and a period of 1 s. The clock is powered by a 200 g weight which falls 2 m between the daily windings. The amplitude of the swing is 0.2 rad. What is the Q (quality factor) of the clock? How long would the...

Homework Statement consider a system with a damping force undergoing forced oscillations at an angular frequency ω a) what is the instantaneous kinetic energy of the system? b) what is the instantaneous potential energy of the system? c) what is the ratio of the average kinetic energy to the...

Homework Statement A damped harmonic oscillator is displaced a distance xo from equilibrium and released with zero initial velocity. Find the motion in the underdamped, critically damped, and overdamped case. Homework Equations d2x/dt2 + 2K dx/dt + ω2x = 0 Underdamped: x =...

Hello, I am confused about how to show that any two solutions of the damped harmonic oscillator equation equal another solution. Thanks!

Homework Statement https://www.physicsforums.com/attachment.php?attachmentid=39373&stc=1&d=1317244721 Homework Equations In all honesty I am not sure? The Attempt at a Solution This question was used as a worked example in my first tutorial for Dynamics. The lecturer didn't break it down...