Damped Definition and 354 Threads

[FONT="Arial Black"]Damped vibration m \frac{d^2x}{dt^2} + \gamma \frac{dx}{dt} + kx = 0 Characteristic equation is mr^2 + \gamma r + k = 0 r_1 = \frac{- \gamma + \sqrt{( \gamma )^2 - 4mk}}{2m} r_2 = \frac{- \gamma - \sqrt{( \gamma )^2 - 4mk}}{2m} In overdamped ( \gamma )^2 -...

Hi everyone, I'm dealing with system identification for the first time in my life and am in desperate need of help :) The system is spring-mounted and I'm analyzing the vertical and torsional displacements. However, it seems like the vertical and torsional oscillations are coupled (shouldn't...

the formula for damped oscillations is given as x = Ae^(-bt/2m) cos(ωt+Φ) so why is the amplitude as a function of time given as only the first part? meaning only A(t) = Ae^(-bt/2m) it "ignores" the 2nd term which is the oscillating cosine term. which still encompass a time t value...

My textbook gives the equation A=Ao(e^-bt/2m) for the changing amplitude of damped oscillations. What I don't understand is where this equation comes from. Why make it to the base e? Why not make the equation A=Ao(f^T/t) where f is the factor by which it is decay and T is the period.

Homework Statement The frequency f[SIZE="1"]d of a damped oscillator is 100 Hz, and the ratio of the amplitudes of two successive maxima is one half. What is the undamped frequency f[SIZE="1"]0 of this oscillator?Homework Equations this is the equation in my textbook for the position at time t...

Homework Statement "Show that the ratio of two successive maxima in the displacement of a damped harmonic oscillator is constant."Homework Equations x = a e^(-\upsilont/2) cos (\omegat - \vartheta)The Attempt at a Solution So I want to find when this beast has its maximum values, so I take the...

Differentiation of damped motion function - Need help urgently! Homework Statement Basically my task was to come up with a function to model the swing of a pendulum. The model I came up with was: 0.16e^{-0.25t}cos((\stackrel{2\pi}{1.22})t-0.8) + 0.814 The next part of my task asks me...

Homework Statement A mass M is suspended from a spring and oscillates with a period of 0.880 s. Each complete oscillation results in an amplitude reduction of a factor of 0.96 due to a small velocity dependent frictional effect. Calculate the time it takes for the total energy of the...

the solution for current I, for series LCR circuit is I = (E/Z)sin(wt+\phi) Where Z = \sqrt{R^2 + (X_{L}-X_{C})^{2}} So for Resonance (i.e. maximum Current Amplitude) of LCR Circuit the necessary condition seems to be X_{L}=X_{C} Which gives \omega=1/\sqrt{LC} But some text-books and wikipaedia...

This may straddle more advanced physics, but I thought it leaned toward introductory. Homework Statement I have been told to find the net energy of a damped pendulum. Homework Equations Obviously the equation of energy for an undamped pendulum is just: E = KE + PE = .5mv^2 + mgh = 0 I...

Interest in 3D Lissajous Figures lead to a Google search which lead to a free program which ran on the free program, Mathematica Player, from Wolfram research, http://www.wolfram.com/products/player/ From that page, " Mathematica Player is an innovative new take on viewer applications...

Hi all I'm not sure if this question is better suited for the EE thread or diff eq, but I'm trying to understand what the neper frequency, \alpha, signifies. I know it's supposed to be the damping factor and that its units are rad/second, but I'm not sure what that implies. It would seem to...

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.

Hi.. I'm trying to do the damped vibration analysis of a cantilevered beam. Although i am choosing no damping in subdomain settings menu, it solves the problem as if the material is damped (the result is a damped vibration signal). Is this is a bug or am i missing something? Thanks in advance

Homework Statement A 45.0-g hard boiled egg moves on the end of a spring with a force constant k = 2.50 N/m. Its initial displacement is 0.500 m. A damping force Fx = -bvx acts on the egg, and the amplitude of the motion decreases to 0.300 m in 4.0 s. Calculate the magnitude of the damping...

Homework Statement A 50.0g hard-boiled egg moves on the end of a spring with force constant k = 25.0 N/m. It is released with an amplitude 0.300m. A damping force Fx = -bv acts on the egg. After it oscillates for 5.00s, the amplitude of the motion has decreased to 0.100m. Calculate the...

1. SDOF Systems Governing Equation m(dx^2/dt^2) + c(dx/dt)+ kx = F(t) how do i get this equation below? Free Critically damped Vibration x(t) = e^(wt) [x(0)(1+wt) + (dx/dt)(0) t] (dx/dt is x with 1 dash on top)

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 Hi guys the question is: a mass spring-damper system is positioned between two rigid surfaces, if mass m = 200g, spring constant k = 80 Nm-1, and damping pot of coefficient 65 gs-1. The mass is pulled 5cm down from its equilibrium position and then released. What is the...

Matlab, how to find damped frequency of a sate space matrix euqation? Hello: I am working on a tyre mechanic problem basically it just a vibration problem so far I have dervied the the state space equation which is in the form x'=[A]x+[B]u [A] is 2x2 matrix, [B] is a 1X2 matrix (u...

Homework Statement A heavily damped simple harmonic system is displaced a distance F from its equilibrium positio and released from rest. Show that in the expression for the displacement x=e^{-pt}(F\cosh qt + G\sinh qt) where p=\frac{r}{2m} and...

How do you use separation of variables to solve the damped wave equation y_tt + 2y_t = y_xx where y(0,t) = y(pi,t) = 0 y(x,0) = f(x) y_t (x,0) = 0 --- These are partial derivatives where y = X(x)T(t) So rewriting the equation I get X(x)T''(t) + 2X(x)T'(t) = X''(x)T(t) which...

Hi all! I was considering the Energy of a driven damped oscillator and came upon the following equation: given the equation of motion: m\ddot x+Dx=-b\dot x+F(t) take the equation multiplied by \dot x m\ddot x\dot x+Dx\dot x=-b\dot x^2+F(t)\dot x and we rewrite it...

damped harmonic oscillator, urgent help needed! Homework Statement for distinct roots (k1, k2) of the equation k^2 + 2Bk + w^2 show that x(t) = Ae^(k1t) + Be^(k2t) is a solution of the following differential equation: (d^2)x/dt^2 + 2B(dx/dt) + (w^2)x = 0 Homework Equations The...

Homework Statement Not actually a homework problem, just something from my book I'm trying to verify. Homework Equations The general form of the equation for damped oscillations... \ x(t) = e^{-\gamma t}(Ae^{\sqrt{\gamma^{2}-\omega^{2}}t}+Be^{-\sqrt{\gamma^{2}-\omega^{2}}t}) Here gamma =...

I am trying to understand the analogy between a particle resonance and the resonance in a driven, damped classical oscillator. I guess I should first ask for a clear definition of a particle resonance - is this just an excited state which decays quickly? I understand that the KG equation...

I am not sure that I understand what damped harmonic oscillation is different from simple harmonic oscillation, can someone please explain that to me? I read wikipedia and still doesn't get it...

I have trouble understanding how damping affects the period (of a torsion pendulum). I know that damping affects the amplitude of the oscillator, however how would damping change the period then? I have a feeling this has to do with angular frequency, w, given by: w = sqrt( (k/m) -...

Homework Statement This problem was presented as part of a lab write up. In the lab we were studying damped oscillations. We were asked to determine the mass indirectly based on values that we measured then compare it to the actual masses. We found that the calculated masses were much greater...

Homework Statement I have read the chapter twice and I have read through the notes several times to help me with the homework assignment. It deals with damped Harmonic Oscillations. Problem: You have a mass submerged horizontally in oil and a spring with a k of 85 N/m pulls on a mass of...

Homework Statement A damped harmonic oscillator originally at rest and in its equilibrium position is subject to a periodic driving force over one period by F(t)=-\tau^2+4t^2 for -\tau/2<t<\tau/2 where \tau =n\pi/\omega a.) Obtain the Fourier expansion of the function in the integral...

Hi, I am trying to solve the damped harmonic oscillator: \frac{d^2y}{dt^2}+\frac{b}{m} \frac{dy}{dt}+\frac{k}{m}y=0 and I thought using the Laplace transform might do the trick. Anyway so I did the LT (and inserted the initial conditions that at t=0 y=A, and dy/dt=0) and obtained...

Homework Statement Marie observes damped oscillations of a glider on an air track. She observed that the amplitude decreased to 50% of its original value after 10 seconds. What is the decay constant for the motion of the glider? Homework Equations The Attempt at a Solution It...

Homework Statement Find the general solution of the damped SHM equation(5.9) for the special case of critical damping , that is , when K = \Omega. Show that , if the particle is initially relaeased from rest at x= a , then the subsequent motion is given by x=a*(e^-(\Omega*t))*(1+\Omega*t)...

Homework Statement A damped oscillator satisfies the equation x'' + 2Kx' + \Omega^2 *(x) where K and \Omega are positive constants with K < \Omega (underdamping). i)At time t =0 the particle is released from rest at the point x=a . Show that the subsequent motion is given by...

Qn2 The amplitude of a lightly damped osciallator decreases by 3% during each cycle of oscillation. What fraction of the energy is lost in each cycle? Okay..i couldn't find anything about energy in the damped oscillation is my textbook.. but in SHM sections. it showed that Energy of...

man..i have 5 questions on SHM with damping..and it so difficult..it seem that the book have little coverage on this.. Qn1 A system, which is critically damped, has zero displacement at time t=0 and receive an impulse which gives it an intially velocity V. Obtain an expression for the...

Doing a Cascade Control lab and I'm stuck on a question. Its asking me how to implement critically damped into a control system. I can't find it any where in my books or the net. thanks.

The equation for motion for a damped oscillator is: x(double dot) + 2x(dot) + 2 = 0 a) Show that x(t)= (A + Bt)e^-t Where A and B are constants, satisfies the equation for motion given above. b) At time t = 0, the oscillator is released at distance Ao from equilibrium and with a...

Homework Statement Hello, I got to solve the following second order transient circuit. Obviously, what I need to do first is to find if its critically damped, underdamped, or overdamped. The circuit can be found in the attachment. Homework Equations Depends, weather the circuit is...

Homework Statement A sinusoidally varying driving force is applied to a damped harmonic oscillator of force constant k and mass m. If the damping constant has a value b_1, the amplitude is A_1 when the driving angular frequency equals sqrt (k/m). In terms of A_1, what is the amplitude for...

Hi everyone. I have a project where I need to find a situation this is, or is similar to, a damped oscillator. That is, the Differential Equation (DE) for the system must follow: x'' + ax' + bx = 0 And, further, it must have some situation corresponding to being 'driven' or 'forced', that...

Working through my lecture summaries, I have been given that Q (the quality factor) =\frac{2\pi}{(\Delta E/E)cycle} and accepted this as a statement, taking \((\Delta E/E)cycle} to mean the 'energy loss per cycle'. The notes carry on to say 'The frequency \widetilde{\omega} of...

Homework Statement Hi. The problem is question 1(a) in the file below: http://www.mth.uct.ac.za/Courses/MAM24678/mod2od/Project1_07.pdf The Attempt at a Solution Question 1(a) is the one I have a problem with. I just don't know what he's getting at. Is y(x) the function that describes...

[SOLVED] Lightly damped spring system Q Homework Statement Consider a lightly damped mass-on-a-spring vibrational system. How should motion be initiated so that the amplitude of the spring is given by; \Psi(t)=Ce^{-\frac{\lambda}{2}t}Cos(\omega_{r}t+\pi) Homework...

Concerning damped harmonic motion (eg. mass on a spring, using cardboard discs as dampers); for the equation (below) of the graph describing the effect of different sized dampers on the time taken for amplitude of oscillations to halve, what would b (y-intercept) and n (gradient) represent...

1. Homework Statement Plot total energy vs. time graph using MATLAB (damped system) wn(the undamped natural frequency) = 2 rad/s damping ratio, z = 0.01 mass = 10kg initial displacement = 0.1 initial velocity = 0 2. Homework Equations KE = (1/2)mv^2 PE = mgh 3. The Attempt...

Homework Statement Concerning damped harmonic motion (mass on a spring using cardboard discs as dampers); for the equation (below) of the graph describing the effect of different sized dampers on the time taken for amplitude of oscillations to halve, what do b (y-intercept) and n (gradient)...

[SOLVED] Stuck on damped pendulum question... Homework Statement A pendulum of length 1.00m is released at an angle of 15.0 degrees. After 1000 seconds, it's amplitude is decreased to 5.50 degrees due to friction. What is the value of b/2m? Homework Equations w = \sqrt{w_{0}^{2} -...

Homework Statement A damped oscillator of mass m=1,6 kg and spring constant s=20N/m has a damped frequency of \omega' that is 99% of the undamped frequency \omega. As found out by me: The damping constant b is 0.796 kg/s. Q of the system is 7.1066 kg^-1. Are the units here right? The...