Damped Definition and 354 Threads

Homework Statement A viscously damped system has a stiffness of 5000 N/m, critical damping constant of 0.2 N-s/m, and a logarithmic decrement of 2.0. If the system is given an initial velocity of 1 m/s, determine the maximum displacement. Homework EquationsThe Attempt at a Solution From the...

A viscously damped system has a stiffness of \(5000\) N/m, critical damping constant of \(0.2\) N-s/m, and a logarithmic decrement of \(2.0\). If the system is given an initial velocity of \(1\) m/s, determine the maximum displacement. From the question, we have that \(k = 5000\), \(\delta =...

Hey PF. This isn't a homework question and I'm hoping this is the right place to ask it, sorry if it isn't! In the case of a weakly damped harmonic oscillator driven by a sinusoidal force of the form Fe^(iwt). The form of the differential force equation of motion is then given by ma + cv +kx =...

Question: The damped frequency (f) is 100 Hz. The ratio of the amplitude of two successive maxima is one half. What is the undamped frequency? My first problem is I don't understand the basic equations I'm working with. If W is the undamped angular frequency and w is the damped frequency, I...

Hello Physics Forum! I have a question: The problem: For a lightly damped oscillator being driven near resonance in the steady state, show that the fraction of its energy that is lost per cycle can be approximated by a constant (something like 2pi, which is to be determined) divided by the Q...

Homework Statement A block on a horizontal surface is attached to two springs whose other ends are fixed to walls. A light string attached to one side of the block initially lies straight across the surface. The other end of the string is free to move. There is significant friction between...

Hey PF, my book either got sloppy in a derivation or I am not connecting two very obvious dots. It gives the energy of the damped harmonic oscillator as E = (1/2)mv^2 + (1/2)kx^2 then takes the derivative with respect to time to get dE/dt. then it gives the differential equation of motion...

Homework Statement i can't understand why curve above is for under dampling and the below curve is increased dampling. can someone explain please? https://www.flickr.com/photos/123101228@N03/14296397365/ Homework Equations The Attempt at a Solution

Hiya can anyone show how to derive the euqation of damped frequency for a spring ωd = ωnsqrt(1-ζ2)

Hello, I am working on this problem However, I am getting a 900t term that the solution is lacking. I am wondering if what I did was wrong. My formula is consistent with the formula for a series RLC circuit that is critically damped.

Hi I have a damped simple harmonic motion model and I am altering the input force along with spring constant and damping constant. I can change the damping and spring constant to allow it to oscillate for few seconds before it stops at 0. What parameters do I need to change to alter the...

Hello! I have data of a damped oscillation (the movement on Y as it dies down in time). Imagine for example a ball that is hanging from a spring and it keeps bouncing up and down under the spring until it stops. The problem is I do not know how to find the axis around which the oscillation...

Hi I am trying to model SHM in Simulink as shown here: http://pundit.pratt.duke.edu/wiki/Simulink/Tutorials/DiffEq I have tried using different values of spring constant and damping to get instant response to the input force. I am measuring the displacement calculated by SHM. The force changes...

Homework Statement The equation for a damped oscillation is y(t)=Ae^{-\frac{b}{2m}t}cos(\omega't + \phi) We know that y(0)=0.5 and y'(0)=0. Find the values of A and ø and then plot the oscillation in MATLAB. Homework Equations See above The Attempt at a Solution When...

Hello, I'm trying to analyze a system of elastically coupled oscillators, whose masses are all the same, using Fourier expansion. So the differential equation I am looking at right now is of the form m\frac{d^2\hat{y}_k}{dt^2} + \gamma\frac{d\hat{y}_k}{dt} - \kappa\Delta^2\hat{y}_k =...

Homework Statement Hi, so my question is about a damped simple harmonic motion experiment The experiment is as follows: A 30 cm ruler with a needle attached to it is clamped to a bulldog clamp. The needle is placed in a beaker of water so that it is just inside the water ( by about...

The standard equation for the damped angular frequency of a normal damped mass-spring system is ω_{d} = \sqrt{\frac{k}{m}-\frac{b^{2}}{4m^{2}}}. Let p=\frac{b}{2m}, we have ω_{d} =\sqrt{ω_{0}^{2}-p^{2}} Now consider that damped mass-spring system being driven by a periodic force with the...

For a damped mechanical oscillator, the energy of the system is given by $$E = \frac{1}{2}m \dot{x}^2 + \frac{1}{2}k x^2$$ where ##k## is the spring constant. From there, I've seen it dictated that the average kinetic energy ##\langle T \rangle ## is half of the total energy of the system. This...

Hey guys I'm new to the forum and having a little trouble with this conceptual problem. 1. 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 of this system: i) If the block is...

Homework Statement Plot x(t) for a damped system of natural frequency w_n= 2 rad/s and initial conditions x_0= 1 mm and v_0 = o mm/s, for the following values of the damping ratio: z= 0.01, 0.2, 0.6, 0.1, 0.4 and 0.8 Homework Equations The Attempt at a Solution I began by defining...

How do I find the transfer function of damped masses hanging? I know that the transfer function is \[ H(s) = \frac{\mathcal{L}\{y(t)\}}{\mathcal{L}\{x(t)\}} \] where \(u\) is the input which is a force and \(x_1\) is the output. Given the following diagram (see below), how do I find the input...

The example I'm thinking of is a mass spring system. x = Ae^(\gamma/2)t cos(wt +a) + Ccos(wt) If the steady state has been reached, the displacement due to the free oscillations will be negligible, so does that mean that the only force acting on the mass is the driving force, F0cos(wt)...

Homework Statement The terminal speed of a freely falling object is v_t (assume a linear form of air resistance). When the object is suspended by a spring, the spring stretches by an amount a. Find the formula of the frequency of oscillation in terms of g, v_t, and a. Homework Equations the...

So we know that SHM can be described as: x(t) = Acos(ωt + ϕ) v(t) = -Aω sin(ωt + ϕ) a(t) = -Aω^2 cos(ωt + ϕ) it can be easily said that the max acceleration (in terms of magnitude) a SHM system can achieve is Aω^2 In Damped Harmonic Motion we know that: x(t) = (A)(e^(-bt/2m))cos(ωt + ϕ) given...

Hi, in this article: http://dx.doi.org/10.1016/S0021-9991(03)00308-5 damped molecular dynamics is used as a minimization scheme. In formula No. 9 the author gives an estimator for the optimal damping frequency: Can someone explain how to find this estimate? best, derivator

Homework Statement (A) The damped oscillator is described by the equation mx''+bx'+kx=0. What is the condition for critical damping expressed in terms of m,b,k. Assume this is satisfied. (B) For t<0 the mass is at rest (x=0). This mass is set in motion at t=0 by a sharp impulsive force so...

Homework Statement The problem is long so I will post the whole thing but ask only for help on part C. The steady-state motion of a damped oscillator driven by an applied force F0 cos(ωt) is given by xss(t) = A cos(ωt + φ). Consider the oscillator which is released from rest at t = 0...

Homework Statement For the forced damped oscillator, show that the following are frequency independent. a) displacement amplitude at low frequencies. b) the velocity amplitude at velocity resonance. c) the acceleration amplitude at very high frequencies Homework Equations...

Homework Statement For a lightly damped harmonic oscillator and driving frequencies close to the natural frequency \omega \approx \omega_{0}, show that the power absorbed is approximately proportional to \frac{\gamma^{2}/4}{\left(\omega_{0}-\omega\right)^{2}+\gamma^{2}/4} where \gamma is...

Homework Statement A mass of 1000 kg drops from a height of 10 m on a platform of negligible mass. It is desired to design a spring and dashpot on which to mount the platform so that the platform will settle to a new equilibrium position 0.2 m below its original position as quickly as possible...

This is the first time I post anything here, so, if I am doing anything wrong about the rules (it is possible that I didn't correctly understand a topic or two), please let me know. This one is a somewhat classic problem of damping, and I can't understand the basic concepts, so I tried to do my...

Homework Statement A single loop circuit consists of a 7.2 ohm resistor, a 11.9 H inductor, and a 3.4*10^-6 F capacitor. Initially the Capacitor has a charge of 6.3*10^-6 C and the current is zero. Find the charge on the capacitor N complete cycles later for N=5.Homework Equations 2. Homework...

The model of damped harmonic oscillator is given by the composite system with the hamiltonians ##H_S\equiv\hbar \omega_0 a^\dagger a##, ##H_R\equiv\sum_j\hbar\omega_jr_j^\dagger r_j##, and ##H_{SR}\equiv\sum_j\hbar(\kappa_j^*ar_j^\dagger+\kappa_ja^\dagger...

Homework Statement A simple pendulum has a length of 1m. In free vibration the amplitude of its swings falls off by a factor of e in 50 swings. The pendulum is set into forced vibration by moving its point of suspension horizontally in SHM with an amplitude of 1 mm. a) [... Built Differential...

Homework Statement A 3.9kg block hangs from a spring with constant 2160 N/m. The block is pulled down 6.2 cm from the equilibrium position and given an initial velocity of 1.5 m/s back towards equilibrium. The mass and spring are now immersed in water to damp the motion, so that the...

Homework Statement This problem was given in my physics test, and my physics teacher was unable to provide me with an answer for it. Given a circuit made up of a generator of variable frequency, i=Im(sin2∏ft-∅) and voltage u=Um(sin2∏ft), capacitor of capacitance 1μF, resistor of resistance...

Homework Statement Homework Equations http://en.wikipedia.org/wiki/Harmonic_oscillator#Damped_harmonic_oscillator The Attempt at a Solution Part a) I believe to find the mass I can use the equation $$ T = 2pi * sqrt( k / m ) $$ with T = 0.6s Part b) I am confused on...

Homework Statement If both k of the spring and m are doubled while the damping constant b and driving force magnitude F0 are kept unchanged, what happens to the curve, which shows average power P(ω)? Does the curve: a) The curve becomes narrower (smaller ω) at the same frequency; b) The curve...

I have a potential well which is an infinite wall for x<0 and a linear slope for x>0. There is damping proportional to velocity. Basically, it's a ball bouncing elastically off the ground and with air friction included. I wonder if there is some periodic driving force which will cause one...

So we are given two equations: $$ \ddot{x} - \dot{x} - x = cost (t) $$ and $$ x(t) = a sin(t) + b cos(t) $$ The question asks to find a and b. How would one go about doing this? I thought maybe substituting the $$ cos(t) $$ from equation 1 into equation 2 would work but then what...

Homework Statement Part (iv) The Attempt at a Solution My attempt is below. Is it correct ? Homework Statement

Homework Statement http://www.mediafire.com/view/?7045cz9au1ci7cd A mountain bike has bad shock absorbers (w0/γ = 10) that oscillate with a period of 0.5 seconds after hitting a bump. If the mass of the bike and rider is 80kg, determine the value of the spring constant k (remembering that...

http://www1.gantep.edu.tr/~physics/media/kunena/attachments/382/chapter2.pdf On page 9 and 10 of the above PDF the method for deriving the fractional energy loss per cycle in a lightly damped oscillator is described. I understand and follow this derivation. What would the derivation...

So my professor was discussing the case of a mass suspended from a vertical massless spring in some viscous liquid. He arrives at the equation of motion which was :x: + \frac{b}{m}x. + \frac{k}{m}x = 0 x: is the second derivative of displacement wrt time. similarly x. is the first derivative...

Homework Statement (A) A damped oscillator is described by the equation m x′′ = −b x′− kx . What is the condition for critical damping? Assume this condition is satisfied. (B) For t < 0 the mass is at rest at x = 0. The mass is set in motion by a sharp impulsive force at t = 0, so...

Homework Statement A mass of 40 g stretches a spring 10 cm. A damping device imparts a resistance to motion numerically equal to 560 (measured in dynes/(cm/s)) times the instantaneous velocity. Find the equation of motion if the mass is released from the equilibrium position with a downward...

Homework Statement A force of 2 lb stretches a spring 1 ft. A 3.2 lb weight is attached to the spring and the system is then immersed in a medium that imparts a damping force numerically equal to 0.4 times the instantaneous velocity. Find the equation of motion if the weight is released from...

Homework Statement Hello everyone. I need to demonstrate that with a damped free oscillator, which is linear, the total energy is a function of the time, and that the time derivative of the total energy is negative, without saying if the motion is underdamped, critically damped or overdamped...

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 $C_n$? $$...