Damped Definition and 354 Threads

[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 =...

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 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...

I have a damped linear oscillator, originally at rest in its equilibrium position [therefore, x(0)=0 and x'(0)=0]. It is subjected to a forcing function: F(t)/m = {0, if t<0 {a(t/tau), if 0<t<tau {a, if t>tau I have to find the response function. However, when I attempt to find the step...

what is the equation? i have something written down in my notes but i really don't get it... x=A(e^-kt)(cos omega t) first of all, how is the amplitude calculated if it decreases over time?? is it averaged? what is e? second of all, to calculate k, you need hooke's law and you need...

I'm having trouble with this problem.The suspension system of a 2100 kg automobile "sags" 7.2 cm when the chassis is placed on it. Also, the oscillation amplitude decreases by 35% each cycle. Estimate the values of (a) the spring constant k and (b) the damping constant b for the spring and shock...

Problem 1: I have a mathematical pendulum with a mass m connected to a string of length l. The pendulum is damped by air resistance that is proportional to the velocity, Ffric = -k*v. I need to derive the damping effect the air resistance has on the pendulum - that is, the decrease of the...

Problem 1: I have a mathematical pendulum with a mass m connected to a string of length l. The pendulum is damped by air resistance that is proportional to the velocity, Ffric = -k*v. I need to derive the damping effect the air resistance has on the pendulum - that is, the decrease of the...

I am really struggling with this question... Question: Consider a damped oscillator, with natural frequency w_0 (omega_0) and damping constant B (beta) both fixed, that is driven by a force F(t)= F_0*cos(wt). Find the rate P(t) at which F(t) does work and show that the average < P > over any...

Hello, On this page: http://galileo.phys.virginia.edu/classes/152.mf1i.spring02/Oscillations.htm It says (and shows) that in the case of a critically damped oscillation, it moves more quickly to zero than in the overdamped case. I don't understand why. The solution to this circuit is...

Here's the problem: A damped oscillator has a mass of .05 kg, a spring constant of 5 N/m, and a damping constant of .4 Ns/m. At t=0, the mass is moving at 3.0 m/s at x=.1m. Find x as a function of time. What I have done: I know the damping constant b = .4 and I have used this to find...

Please I don't understand this problem at all: Consider a driven damped harmonic oscillator.Calculate the power dissipated by the damping force? calculate the average power loss, using the fact that the average of (sin(wt+phi) )^2 over a cycle is one half? Please can I have some help for...

Sorry that I had to use an image file, I was having a lot of trouble using the Latex system. http://www.flamingice.5gigs.com/Question.gif Ok... We know the amplitude of the oscillations, and the force per person, so all we need to do is find Fmax, by finding other values and substituting...

Driven, damped harmonic oscillator -- need help with particular solution Consider a damped oscillator with Beta = w/4 driven by F=A1cos(wt)+A2cos(3wt). Find x(t). I know that x(t) is the solution to the system with the above drive force. I know that if an external driving force applied...

I'm having trouble with this problem. I want to get it into a form with cos but I'm stumped. The solution for damped simple harmonic motion is given by x = (e^(-rt/2m))(C_1*e^(iw't)+C_2*e^(-iwt)) If x = Acos phi at t = 0, find the values of C_1 and C_2 to show that x'=(approx)...

hi guys, doing damped and forced harmonic motion at college at the moment, but i don't do further maths...hence I'm a tad behind compared to those who do (half the class). we don't need to know it for the exam itself, but you know...curiosity. does anyone know of any good online resources...

Hi, I do not know how to drive an experession for energy loss of damped oscillator.I know that: X(t)=A exp(-Beta*t)cos(wt-delta) and: v=dx/dt... I found E=K+U but it seems to be so messy. It is like: E=(1/2)*m*(A^2)*exp(-2*beta*t)[ beta^2 (cos(wt-delta))^2)+beta* sin...

Can you help me start on this one: Show that an overdamped or critically damped oscillator can cross the origin at most once.

Question: (a) Show that the total mechanical energy of a lightly damped harmonic oscillator is E = E_0 e^{-bt/m} where E_0 is the total mechanical energy at t = 0. (b) Show that the fractional energy lost per period is \frac{\Delta E}{E} = \frac{2 \pi b}{m \omega_0} = \frac{2...

i am going to write a report about damped oscillation . as i planned , i will discuss the amplitude decays exponentially with time , application . but that are too little to talk to then what things need to be further discuss? and one question if i use one small card and bid card to damp...

I am confused! Forced oscillation is the one which a periodic force is imposed on a oscillating system. For a damped oscillator, the damping force is proportional to velocity which varies periodically. Does it mean that the damping force is a periodic force and the damped oscillation is a...

Question: A damped harmonic oscillator loses 5.0 percent of its mechanical energy per cycle. (a) By what percentage does its frequency differ from the natural frequency \omega_0 = \sqrt{k/m}? (b) After how may periods will the amplitude have decreased to 1/e of its original value? So, for...

A pendulum of length 1.00 m is released from an initial angle of 18.0°. After 500 s, its amplitude is reduced by friction to 5.5°. What is the value of b/2m? i have no idea how to do this prooblem, the book goes over this section really briefly... what the heck is b/2m?

Hi, I'm having a lot of trouble with a damped harmonic oscillator problem: A damped harmonic oscillator consists of a block (m=2.00kg), a spring (k=10 N/m), and a damping force (F=-bv). Initially it oscillates with an amplitude of 25.0cm. Because of the damping force, the amplitude falls...

i am finding damped SHM difficult to understand can anyone give sugestion as to what coul .do

a damped simple harmonic oscillator has mass m = 260 g, k = 95 N/m, and b = 75 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)? having trouble getting...

I have two problems, the second of which I think I might be solving right. The web program we use to do our homework isn't accepting my answer. It might be the program's fault, but I'm not sure, so I'd like to check. Here's my first problem: Damping is negligible for a 0.131-kg object...

For a simple damped oscillator... \text {Apparently if } \beta \ll \omega_0 } \text { then ...} \omega_d \approx \omega_0[1-\frac {1}{2}(\beta/\omega_0)^2]} Given that: \beta=R_m/2m \text { (where } R_m= \text {mechanical resistance) } \text { and } \omega _d=\sqrt{(\omega...

Question: A damped harmonic oscillar loses 5.0 percent of its mechanical energy per cycle. (a) By what percentage does its frequency differ from the natural frequency \omega_0 = \sqrt{k/m}? (b) After how many periods will the amplitude have decreased to 1/e of its original value? (a) Let E(t)...

Hi I have two questions to ask and hopefully someone could help as I am getting little help from my college and work collegues 1) The work done by an air compressor is given by W = K [ (p1/p2)^(n-1/n) + (p1/p2)^(n-1/n)-2] where p1,p2,n and K are all constants. QUESTION - show that...

In my notes, there are two sentences make me feel strange... As we know, the pendulum whose length equals to that of the friver pendulum, its natural frequency of oscillation if the same of the frequency of the driving one. This is known as resonance oscillation. However, somewhere I found...