Damped Definition and 383 Threads

Homework Statement The drawing to the left shows a mass m= 1.9 kg hanging from a spring with spring constant k = 6 N/m. The mass is also attached to a paddle which is emersed in a tank of water with a total depth of 34 cm. When the mass oscillates, the paddle acts as a damping force given by...

Young and Freedman book Chapter 13 Periodic Motion: In the third papargraph, the author writes that since a damped oscillator naturally vibrates a frequency of omega-prime, then we expect that an application of a driving force with omega close to omega-prime will cause the amplitude to become...

Homework Statement At the natural frequency,ω0 what are the real and imaginary components of Avel(ω) ? Sketch a phasor diagram with the velocity vector and driving force vector,and use this to provide the phase difference between Avel(ω) and the driving force if ω=ω0 (ι.e at resonance)...

Homework Statement If F0= 0 and γ<<2ω0 where γ=b/m, sketch the resulting wave-form for displacement with time.Define Q,the quality parameter,and show on your sketch how the value of Q, influences the waveform Homework Equations mψ'' =-kψ-bψ' +F0exp(-iωt) The Attempt at a Solution...

Homework Statement I have the damped wave equation; u_{tt} = 4 u_{xx} -2 u_{t} which is to be solved on region 0 < x < 2 with boundary conditions; u(0,t) = 2, u(2,t) = 1. i must; 1) find steady state solution u_{steady}(x) and apply boundary conditions. 2) find \theta(x,t)...

Homework Statement In this problem we will investigate a particular example of damped harmonic motion. A block of mass m rests on a horizontal table and is attached to a spring of force constant k. The coefficient of friction between the block and the table is mu. For this problem we will...

My question is that I am asked to find the angular frequency of a spring-mass system. I am given the damping constant, the mass of the object at the end of the spring, the mass of the spring, and the spring constant. I know that angular frequency equals the square root of the spring constant...

A damped harmonic motion starts from rest at time t=0 with displacement A0 has the equation: x(t) = A0/cos (delta)*e^(-t/tau) *cos (w't + delta) w' is the angular frequency, tau is the time constant and delta is given by: tan (delta) = - (1/w' tau) find the time when the maximum...

Hey there forum! Consider a damped oscillation in which the friction force is F=-bυ. What I want to ask is how do you calculate the work done by this force for any x interval along a line and what is the Power of the work done by this force? I already know that Power P of the work done...

Hi to all! I need to solve following equation: \frac{\partial^2 u}{\partial t^2} + 2 \beta \frac{\partial u}{\partial t} -c^2\nabla^2u=0 It describes a damped wave on a x-y plane. 2\beta is damping factor and c is wave speed. I haven't had any luck finding a PDE class that looks...

Hello, I am looking for suggestions, literature, etc., about techniques and theorems useful for comparing improper integrals of functions characterised by a damped oscillatory behaviour. But let me use the following example to introduce in simple terms what I actually mean. Consider the...

Hi, Not sure on where to post this tread since it involved some fluid mechanics and Maths/ Control theory. I have found the response of a ball flouting in a vertical jet stream of air and the result is a highly non linear system. That is, there is different open loop response as the ball...

Homework Statement A block of mass m is connected to a spring the other end of which is fixed. There is also a viscous damping mechanism. The following observations have been made about the system: 1) if the block is pushed horizontally with force = mg, the static compression in the spring...

Two simple pendulums with the same length L but different masses, m1 and m2=2*m1, are set swinging at the same time with the same initial amplitude. Both pendulums are damped by the same force, Fdamp=-\gammas(dot). Eventually, the amplitude of the lighter pendulum decreases to half its initial...

Homework Statement I have an assignment to make a C++ program (I've never seen C++ before, and my professor has never taught it) that makes a set of displacement values corresponding to the motion of a damped oscillator. The function is: x = A*e^{(-\gamma*t/2)} * cos(\omega*t) where...

hi i have no idea how to do it, can some one give me a direction or an outline? A 1.05 kg mass is suspended from a spring, with a spring constant of 161.0 N/m. Find the driving frequency which would cause resonance. all i need is to know where to start from

Homework Statement Consider a damped oscillator, with natural frequency \omega_{o} and damping constant B, both fixed, that is driven by force F(t) = F_{o}cos(\omegat). Verify that the average rate at which energy is lost to the resistive force is mB\omega^2A^2. Homework Equations x =...

Homework Statement Find the frequency that gives the maximum amplitude response for the forced damped oscillator d^{2}x/dt^{2} + 6dx/dt + 45x = 50cos(\omegat) Homework Equations I'm really confused by this problem, but I know that the amplitude can be found by taking the...

hi, i am supposed to solve this excerise and i don't even know where to start. 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...

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 - 4mk > 0 What I...

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 A damped harmonic oscillator has mass m , spring constant k , damping force - cv . (a) Find the ratio of two successive maxima of the oscillations. (b) If the oscillator has Q = 100 , how many periods will it take for the amplitude to decay to 1/ e of it’s initial...

Homework Statement The frequency fd 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 f0 of this oscillator?Homework Equations this is the equation in my textbook for the position at time t of an underdamped...

Homework Statement Given: The amplitude of a damped harmonic oscillator drops to 1/e of its initial value after n complete cycles. Show that the ratio of period of the oscillation to the period of the same oscillator with no damping is given by T(sub d)/T(sub o) = (1 +...

Homework Statement A driven oscillator with mass m, spring constant k, and damping coefficient b is is driven by a force F_{o}cos(\omega t). The resulting steady-state oscillations are described by x(t) = Re{\underline{A}e^{i\omega t}} where: \underline{A} = \frac{F_{0}/m}{(\omega_{o}^{2} -...

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...

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...

Homework Statement A mass of 0.5kg hangs on a spring. When an additional mass of 0.2kg is attached to the spring, the spring stretches an additional .04m. When the 02kg mass is abruptly removed, the amplitude of the ensuing oscillations of the 05 kg mass is observed to decrease to 1/e of its...

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...