Damped Definition and 383 Threads

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...

Homework Statement I'm trying to follow through a derivation involving the equation of motion for the displacement x(t) of a damped driven harmonic oscillator. m\frac{d^{2}x}{dt^{2}}+\gamma x + \beta \frac{dx}{dt}=F_{0}cos(\omega t) Where cos(\omega t) = \frac{1}{2}\left( e^{i \omega...

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...

Homework Statement Hi all, A hard boiled egg, with a mass m=51g, moves on the end of a spring, with force constant k=26N/m. It's initial displacement is 0.300m. A damping force F^{}x=-bv^{}x acts on the egg and the amplitude of the motion decreases to 0.106m in a time of 5.45s. Calculate the...

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...

[SOLVED] Energy of a damped oscillator Homework Statement I simply need to show that the rate of energy for a damped oscillator is given by: dE / dT = -bv^2, where b is the dampening coefficient Homework Equations I am instructed to differentiate the formula: E = 1/2 mv^{2} + 1/2 kx^{2}...

1. The equation of motion is Ma(t) +rv(t) + Kx(t)=0 a) Look for a solution of this equation with x(t) proportional exp(-Ct) and find two possible values of C. Homework Equations 3. No clue... Please help if you can!

If I damp a torsion pendulum, a force will work on it given by F = -k*v, where k is some constant and v is the velocity. My question is, how can I from this calculate the torque, which this affects the torsion pendulum with? I've tried myself, however, I'm sure there's something wrong: For a...

Hi there. I'm having a problem explaining the physical meaning of the symbols in the equation for an underdamped Harmonic oscillator: A*e^{k*t}*sin(w*t) I can see that A is the amplitude of the first swing, which we will not see, since sin(w*t)=0 for t=0. Now k is the damping constant and...

Homework Statement A pendulum has a period of 5seconds. It is damped so that the amplitude falls to one half its original value in 100seconds. What is the Q? I am having trouble relating the Q with the information I have. Period = 5 seconds There are 5 periods ω = 2π/5 Please...

Driven, damped oscillator - URGENT! Homework Statement A driven, undamped oscillator has an amplitude of 3.0cm at a driving frequency of 9 rad/s and an amplitude of 2.4cm at a driving frequency of 7 rad/s. What is the resonant frequency of the oscillator? Homework Equations A =...

Hi all, I'm trying to sketch a unit response of a damped sinusoid an (unnderdamped system). I presume I'll have to differentiate the function such as the following (1 + 1.25e^(-6t)cos(8t+143))u(t) and then find the turning points of the function and then sketch it. However I'm encountering...

My question is why the books on laser always use a damped oscillator as a model for the transitions in a 2-level atom? I didn't find any more resemblance between the two except they both have a fixed upper and lower limit( but for the atom it is energy, for oscillator it is amplitude ) Thanks...

Homework Statement John the door-stopper man sells and installs door-stoppers. He prides himself as being the world's best stopper and guarantees your money back if you can install a better stopper than him. John's secret to door-stopping is that he remembers from his lectures that the...

Homework Statement A mass m moves along the x-axis subject to an attractive force given by 17B^2mx/2 and a retarding force given by 3Bmx', where x is the distance from the origine and B is a costant. A driving force given by mAcos(wt), where A is a constant, is applied to the particle along...

Homework Statement Consider a damped harmonic oscillator. After four cycles the amplitude of the oscillator has dropped to 1/e of its initial value. Find the ratio of the frequency of the damped oscillator to its natural frequency. Homework Equations T=\frac{ 2\pi}{w_1} w_1^2=w_0^2-...

Homework Statement PROBLEM STATEMENT: Under these conditions, the motion of the mass when displaced from equilibrium by A is simply that of a damped oscillator, x = A cos(ω_0t) e^(−γt/2) where ω_0 = K/M, K =2k,and γ = b/M. Later we will discuss your measurement of this phenomenon. Now...

Homework Statement Given: "In a science museum, a 110 kg brass pendulum bob swings at the end of a 15.0-m-long wire. The pendulum is started at exactly 8:00 a.m. every morning by pulling it 1.5 m to the side and releasing it. Because of its compact shape and smooth surface, the pendulum's...

Homework Statement the equation of motion for a damped harmonic oscillator is d^2x/dt^2 + 2(gamma)dx/dt +[(omega0)^2]x =0 ... show that x(t) = Ae^(mt) + Be^(pt) where m= -(gamma) + [(gamma)^2 - (omega0)^2 ]^1/2 p =-(gamma) - [(gamma)^2 - (omega0)^2 ]^1/2 If x=x0 and...

Homework Statement Show that the fractional energy lost per period is \frac{\Delta E}{E} = \frac{2\pi b}{m\omega_0} = \frac{2\pi}{Q} where \omega_0 = \srqt{k/m} and Q = m\omega_0 / b Homework Equations E = 1/2 k A^2 e^{-(b/m)t} = E_0 e^{-(b/m)t} The Attempt at a Solution \Delta E = 1/2 k A^2...

Hey guys, using my knowledge of y=(e^ax) sin bx and y=(e^ax) cos bx, I need to find an example where these functions could be used as a model. I was thinking about damped harmonic motion but had a tough time trying to find an example and how i could relate it to those two graphs, any ideas?

Homework Statement If the amplitude of a damped oscillator decreases to 1/e of its initial value after n periods, show that the frequency of the oscillator must be approximately [1 - (8(π^2)(n^2))^-1] times the frequency of the corresponding undamped oscillator.Homework Equations Damped...

A mass m moves along the x-axis subject to an attractive force given by \frac {17} {2} \beta^2 m x and a retarding force given by 3 \beta m \dot{x}, where x is its distance from the origin and \beta is a constant. A driving force given by m A \cos{\omega t} where A is a constant, is applied to...

Homework Statement Show that the area in phase space of a cluster of orbits for the damped simple harmonic oscillator given in the lecture varies in time as: A(t) = A(0) e^{(-r/m)t}Homework Equations \dot{x} = (1/m) y \dot{y} = -kx - (r/m) y The Attempt at a Solution I don't understand the...

Driven Damped Harmonic Oscillator, f != ma?? Let's say I've got a driven damped harmonic oscillator described by the following equation: A \ddot{x} + B \dot{x} + C x = D f(t) given that f = ma why can't I write A \ddot{x} + B \dot{x} + C x = D ma substitute \ddot{x} = a to get A \ddot{x}...

I'm trying to find the work done by a harmonic oscillator when it moves from x_{0} = 0 m to x_{max} = 1 m. The oscillator has initial velocity v_{0}, a maximum height of x_{max} = 1 m, initial height of x_{0} = 0 m, a spring constant of k, a mass of m = 1 kg, and a damping factor of b. It can...

Is it possible to express the total energy of a damped linear oscillator as a function of time? I'm confused here. I'd like to find E(t). As the oscillation is damped, dE/dt should everywhere be negative (energy being dissipated as radiation or heat). By setting E(t) equal to zero, shouldn't I...

A critically damped system is one in which the system does not oscillate and returns to its equilibrium position without oscillating. Even, in an overdamped system the system does not oscillate and returns to its equilibrium position without oscillating but at a slower rate compared to...

A weight of mass m = 300 g hangs vertically from a spring that has a spring constant k = 1.50 N/m. The mass is set into vertical oscillation and after 28 s you find that the amplitude of the oscillation is 1/10 that of the initial amplitude. What is the damping constant b associated with the...