Damped Definition and 354 Threads

Homework Statement The equation for a damped oscillator is d2x/dt2+2βdx/dt +ω02 x = 0. Let ω0=1.0 s−1 and β = 0.54 s−1. The initial values are x(0) = x0 and v(0)=0. Determine x(t)/x0 at t = 2π/ω0. Homework Equations the solution to equation is given by...

Homework Statement The logarithmic decrement δ of a lightly damped oscillator is defined to be the natural logarithm of the ratio of successive maximum displacements (in the same direction) of a free damped oscillator. That is, δ = ln(An/An+1) where An is the maximum displacement of the n-th...

Homework Statement The logarithmic decrement δ of a lightly damped oscillator is defined to be the natural logarithm of the ratio of successive maximum displacements (in the same direction) of a free damped oscillator. That is, δ = ln(An/An+1) where An is the maximum displacement of the n-th...

in a spring mass damper system subjected to a periodic force. the response of the system only depends on the force and the restoring forces caused due to the spring is ignored because the damper is assumed to have taken care of it. now it's here that my confusion originates. in a damped free...

So, in lectures we derived the equation for damped SHM by solving the differential equation relating position (x), mass (m), spring constant (s), and damping coefficient (r): m\ddot{x}=-\frac{s}{m}x-r\dot{x} Using a solution of the form Ae^{\alpha t}, we find that: x=Ae^{-pt}e^{\pm qt}...

Homework Statement I figure I will just combine these two questions into one topic. 1) The energy stored in a capacitor is .5CE^2, where E is the voltage. Wat is the instantaneous power dissipated in a resistor R through which this capacitor discharges? Show that the total energy dissipated...

Hi there, I just started an intermediate classical mechanics course at university and was smacked upside the head with this question that I don't know how to even start. Homework Statement We are to find the response function of a damped harmonic oscillator given a Forcing function. The...

Homework Statement a block of mass m=.5kg is sliding on a horizontal table with coefficients of static and kinetic friction of .8 and .5 respectively. It is attached to a wall with a spring of unstretched length l=.13m and force constant 200 n/m. The block is released from rest at t=0 when...

Homework Statement There is a block attached to the wall via a spring. The only damping force is friction, where there is kinetic and static. Homework Equations m(d^2x/dt^2)=-kx-? The Attempt at a Solution I can solve this, except usually the damping force is given as...

Firstly, I spoke to a Physics teacher and some strangers on the internet as well as Googled and this is the situation I am in now. I want to build a software simulation for school of a damped-oscillation non-zero charged metallic-sphere pendulum within the uniform electric field of a...

Homework Statement A 100g mass is suspended on a rubber band with a k coefficient of 2.74 N/m. The original amplitude of the oscillations is 5cm and after 100 oscillations, the maximum speed of the weight is 0.13 m/s. Find the damping coefficient y. Homework Equations d2x/dt2 + γdx/dt...

Homework Statement [PLAIN]http://img848.imageshack.us/img848/1150/damped.png Homework Equations The Attempt at a Solution Part i) x(t) = C1coswt + C2sinwt dx/dt = -C1wsinwt +C2wcoswt using IC's: xo = C1 dxo/dt = C2w therefore x(t) = xocoswt + (dxo/dt)/w sinwt but...

Homework Statement A Force F(t) = F0(1 - e-at), where both F0 and a are constants, acts over a damped oscillator. In t = 0, the oscillator is in it's equilibrium position. The mass of the oscillator is m, the spring constant is k = 2ma2 and the damping constant is b = 2ma. Find x(t)...

Hi I tried 3Dplot Damped spring(steel spring,oil damper) in two sotwares ,and get odds results . Which one is right? In "Maxima gnuplot engine" In "WolphramAlpha engine"

Homework Statement A 200 g oscillator in a vacuum chamber has a frequency of 2.0 Hz. When air is admitted, the oscillation decreases to 60% of its initial amplitude in 50 s. How many oscillations will have been completed when the amplitude is 30% of its initial value? Homework...

Homework Statement I've been given (or have calculated) the equation for damped SHM of a spring, and have been told to calculate the period... I'm given that: Forced produced by damper: b(dx/dt) where b = 16N/ms k = 344.5N/m m = 2kg Homework Equations I know that T = 2*pi/(W0)...

Homework Statement A critically damped oscillator with natural frequency \omega starts out at position x_0>0. What is the maximum initial speed (directed towards the origin) it can have and not cross the origin? Homework Equations For the case of critical damping...

1. An oscillator with mass 0.5 kg, stiffness 100 N/m, and mechanical resistance 1.4 kg/s is driven by a sinusoidal force of amplitude 2 N. Plot the speed amplitude and the phase angle between the force and speed as a function of the driving frequency and find the frequencies for which the phase...

Damping is negligible for a 0.121 kg mass hanging from a light 6.55 N/m spring. The system is driven by a force oscillating with an amplitude of 1.45 N. At what frequency will the force make the mass vibrate with an amplitude of 0.465 m? There are two possible solutions, enter one of them...

I need to calculate the transfer function of a 4 DOFs system, in particular I need to calculate the system natural frequencies. Do you know to figure out these? On books I have found how to get it in the undamped case. Thanks

Ok, there's a bit I don't understand in my lecture notes. The maths doesn't seem to quite work out. Any help would be appreciated. Here's the section I'm confused about: http://img228.imageshack.us/i/physy.jpg/ It's the transition from the second last line of working to the last line which I...

Homework Statement I have a under-damped vibration equation (below) that plots displacement vs time graph. Thing is i need to plot an envelope of the graph and it has to take into account initial speed v0. Homework Equations 1. Equation which plots displacement vs time. x(t)=exp^(-zeta*Wn*t) *...

Homework Statement I need to find the time constant, tau, Homework Equations WILL EDIT THIS TOMORROW Bleeping FMS giving me major brainache *saddest face ever* A(t) = A_0 times e^-t/tauThe Attempt at a Solution I have had numerous attempts and I just fried my (fibromyalgic) brain out with...

Homework Statement A spring with spring constant 17.0 N/m hangs from the ceiling. A 530 g ball is attached to the spring and allowed to come to rest. It is then pulled down 7.00 cm and released. What is the time constant if the ball's amplitude has decreased to 3.50 cm after 41.0...

I'm doing a research project on collisions and I've come across a part of my theory that requires solutions to coupled damped oscillators. Could anyone please refer me to some text on 2 coupled damped oscillators which isn't extremely math heavy and has conceptual explanations of the...

hi all i have a problem in finding the quality factor of cantilever beam (one end is fixed and other end is free ) vibrating in air /other medium? how the qualtiy factor expression for beam is calculated? whether all these expressions applicable to micro and nano cantilevers. please explain...

hi all i have a problem in finding the quality factor of cantilever beam (one end is fixed and other end is free ) vibrating in air /other medium? how the qualtiy factor expression for beam is calculated? whether all these expressions applicable to micro and nano cantilevers. please explain...

Homework Statement The amplitude of an oscillator decreases to 36.8% of its initial value in 10.0 s. What is the value of the time constant? Homework Equations xmax=Ae^-bt/2m Time constant= m/b xmax(t)= Ae^-t/2(timeconstant) The Attempt at a Solution I'm not quite sure where to...

How do I fit the data given below into the standard form (ignore the part saying to use MathCad): http://screensnapr.com/u/apmqkd.png {{{0.002, 0.726}, {0.022, 0.739}, {0.042, 0.75}, {0.062, 0.759}, {0.082, 0.768}, {0.102, 0.776}, {0.121, 0.785}, {0.141, 0.794}, {0.161, 0.802}...

Homework Statement Given a simple pendulum with a mass on the end and a massless string. The support point for the pendulum is moved laterally with an amplitude D at the resonant frequency. The damping is from the air and is considered viscous i.e. not turbulent. The difference between the...

Hi, I have a question about damped oscillator. Actually, although I have read courses about oscillator, I couldn't solve this. I think this is very easy question :( 1. Homework Statement Consider the solution for the damped ( but not driven ) oscillator, x =...

Tuning forks are lightly damped SHO's. Consider a tuning fork who's natural frequency is f=392Hz. Angular frequency = w = 2(Pi)f = 2463 (rad/s) The damping of this tuning fork is such that, after 10 sec, it's amplitude is 10% of it's original amplitude. Here is my attempt to find the damping...

Homework Statement Let ay'' + by' +cy = R(x) Determining whether a system is under/over/critically damped depends on the size of b^2 compared to 4ac. Does it depend at all on R(x)? Homework Equations Characteristic equation, quadratic equation. The Attempt at a Solution...

I am having trouble finding out what the equation for damped harmonic motion is. I have been researching around there there are many small variations on the exponents. I am conducting an experiment which has involved the use of the spring constant from Hooke's Law and have used a hypothesis...

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)...

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...

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...