Damped Definition and 354 Threads

If you consider b^2/m > 4*k, you can get the solution by using classic method (b = damping constant, m = mass and k = spring constant) otherwise you have to use complex numbers. How have the references books proved the solution for this differential equation?

Homework Statement The car circulates on a section of road whose profile can be approximated by a sinusoidal curve with the wavelength of 5.0 m. The mass of the car is 600.0 kg, and each wheel is equipped with a constant spring k = 5000 Nm-1 and a damper with constant b = 450 Nm-1s. Calculate...

Homework Statement Homework EquationsThe Attempt at a Solution After the release the block will move towards right and friction will be towards the left. ##M\ddot x = f - kx## Solving for ##x##, ##x = A\cos (\omega t) + B\sin(\omega t) + f/k## Initial conditions are ##x(0) = x_0, \dot...

hilbert2 submitted a new PF Insights post Damped Motion in Classical and Quantum Mechanics Continue reading the Original PF Insights Post.

Homework Statement The acceleration amplitude of a damped harmonic oscillator is given by $$A_{acc}(\omega) = \frac{QF_o}{m} \frac{\omega}{\omega _o} \sqrt{\it{R}(\omega)}$$ Show that as ##\lim_{\omega\to\infty}, A_{acc}(\omega) = \frac{F_o}{m}## Homework Equations $$\it{R}(\omega) =...

Homework Statement You got a plate hanging from a spring (hookes law: k) with a viscous force acting on it, -bv. If we place a mass on the plate, gravity will cause it to oscillate. Prove that if we want the plate to oscillate as little as possible (Crticial damping, no?), then $$b=2m...

Homework Statement Solve the damped harmonic motion system \ddot{x} + 2k\dot{x} + \omega^2 x = 0 with initial conditions \dot{x}=V at x = 0 in the cases (i) \, \omega^2 = 10k^2 (ii) \omega^2 = k^2 (iii) \omega^2 = 5, k = 3 Identify the type of damping, sketch the curve of x versus t>0 in...

Homework Statement http://imgur.com/a/lv6Uo Homework Equations Look below The Attempt at a Solution I was unsure where to start. I thought that parseval's theorem may be helpful. I know the Potential energy is equivalent to .5kx^2 and T will be the integral of the force. So i have $$<E> =...

Homework Statement Hello all, I have a question regarding the damping constant for a model of a vertically oscillating mass on a spring. I have read through one or two similar questions on this site but I think I can manage to be a little more specific about what I'm asking. I am in a physics...

We can't see objects from objects far away from us. Why? I think light waves damps! When it reaches our eyes it's amplitude is too small to be visualised! Is this true? If indeed EM waves are damped then why? If not please give a suitable definition for the mentioned phenomena too !

Homework Statement I am trying to follow a paper, https://arxiv.org/pdf/1410.0710v1.pdf, I want to get the results obtained in equations 5 and 6 but can't quite work out how eq 3 has been diagonalized. Homework Equations eq 3 The Attempt at a Solution As the system is driven i thought I'd...

So it is a known fact that the Andromeda galaxy will collide and merge with the Milky Way galaxy. In the video it shows the collision. Time 1:40 My question is how does it take only 3 collisions for the merger to take place? First all, can we assume that if no stars/dark matter/planets from...

Homework Statement Force F = const is applied to H.O. initially at rest with mass m, freq w0, damping T. Find x(t). Find work as function of time. Homework Equations mx'' + Tx' + kx = F for F= Constant The Attempt at a Solution First obtain complimentary solution for free H.O. which I get...

Homework Statement A damped harmonic oscillator consists of a block (m = 2.72 kg), a spring (k = 10.3 N/m), and a damping force (F = -bv). Initially, it oscillates with an amplitude of 28.5 cm; because of the damping, the amplitude falls to 0.721 of the initial value at the completion of 7...

Homework Statement A damped harmonic oscillator is driven by an external force of the form $$F_{ext}=F_0sin(\omega t)$$ Show that the steady state solution is given by $$x(t)=A(\omega)sin(\omega t-\phi)$$ where $$ A(\omega)=\frac{F_0/m}{[(\omega_0^2-\omega^2)^2+4\gamma^2\omega^2]^{1/2}} $$ and...

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 \frac {T_d} {T_0} = \sqrt {1+ \frac {1}...

Homework Statement Evaluate the Fourier Transform of the damped sinusoidal wave g(t)=e^{-t}sin(2\pi f_ct)u(t) where u(t) is the unit step function. Homework Equations \omega =2\pi f G(f)=\int ^{\infty}_{-\infty} g(t)e^{-j2\pi ft}dt sin(\omega _ct)=\frac{e^{j\omega _ct}-e^{-j\omega _ct}}{2j}...

Hi,I need help please, i want to know how to solve de differential equation of a system of two degree of freedom using eigenvalues or eigenvectors or if I can use any another way to solve this kind of equations.

Hi,I need help please, i want to know how to solve de differential equation of a system of two degree of freedom using Heigenvalues or Heigenvectors or if I can use any another way to solve this kind of equations.

Homework Statement The expression for electric charge on the capacitor in the series RLC circuit is as follows: q(t)=A*exp(-Rt/2L)*cos(omega*t+phi) where omega=square_root(1/LC-R^2/4L^2) What is the phase phi, if the initial conditions are: q(t=0)=Q I(t=0)=0 Homework Equations The damped...

Homework Statement I am supposed to calculate Lyapunov exponent of a damped, driven harmonic oscillator given by ## \ddot{x} + 2\beta \dot{x} + \omega_0^2 x = fcos(\omega t)## Lyapunov exponent is ## \lambda ## in the equation ## \delta x(t) = \delta x_0 e^{\lambda t} ## The attempt at a...

Homework Statement Hi everybody! I'm doing a problem about oscillations, and I must admit that a few things are still unclear to me about that subject. Can someone maybe help me? a) A onedimensional masspoint m is oscillating under the influence of the force F(x) = -c⋅x (c > 0). What is the...

Homework Statement On June 10, 2000, the Millennium Bridge, a new footbridge over the River Thames in London, England, was opened to the public. However, after only two days, it had to be closed to traffic for safety reasons. On the opening day, in fact, so many people were crossing it at the...

Afternoon All I have a math question I don't actually have a clue what to do. Can some help me out. A mass M is suspended vertically by a damped spring of length L and stiffness k such that the distance x between the centre of the mass and the top of the springis given by M (d^2 x)/(dt^2...

I uploaded a picture of what I am stuck on. I understand the equation of motion 3.4.5a for a damped oscillator but I don't understand how to use binomial theorem to get the expanded equation 3.4.5b. I am no where near clever enough to figure this one out. I know how to use binomial theorem to...

Homework Statement consider any damped harmonic oscillator equation m(d2t/dt2 +bdy/dt +ky=0 a. show that a constant multiple of any solution is another solution b. illustrate this fact using the equation (d2t/dt2 +3dy/dt +2y=0 c. how many solutions to the equation do you get uf you use this...

Homework Statement Homework EquationsThe Attempt at a Solution I'm working on part a. The numerical value of Q. I have an equation stating that Q = ω_0/ϒ. I don't really know what ϒ is, in other places (http://farside.ph.utexas.edu/teaching/315/Waves/node13.html) it seems like the...

Homework Statement The amplitude of a simple pendulum oscillating in air with a small spherical bob, decreases from 10 cm to 8 cm in 40 seconds. Assuming that Stokes Law is valid, and ratio of the coefficient of viscosity of air to that of carbon dioxide is 1.3, the time in which amplitude of...

Homework Statement Homework EquationsThe Attempt at a Solution I'm not really sure how to go about this. They tell me the hint, and to use the simplification. I assume when they say (1+y)^n they take y to be in general, anything. It was confusing at first to see a y in the format when no y...

Homework Statement Verify that Ae^(-βt)cos(ωt) is a possible solution to the equation: d^2(x)/dt^2+ϒdx/dt+(ω_0)^2*x = 0 and find β and ω in terms of ϒ and ω_0. Homework Equations N/a, trig identities I suppose. The Attempt at a Solution I think this is simply a 'plug and chug' type...

Modeling driven undamped spring systems in my diff eqs text at the moment. So I've just worked through the derivation of x(t) = C\cos{(\omega_0t - \alpha)} + \frac{F_0/m}{\omega_0^2-\omega^2}\cos{\omega t} And it's clear that this describes the superposition of two different oscillations...

Homework Statement Given the IVP \ddot{r}+\dot{r}+20r=0\\ r(0) = 0.8\\ \dot{r}(0) = 0 for the length of an oscillating spring (damped), we find that the general solution is r=e^{-0.5t}[0.8\cos(\sqrt{19.75}t)+\frac{0.4}{\sqrt{19.75}}\sin(\sqrt{19.75}t)] and I wish to find the curve bounding...

Homework Statement A gong makes a loud noise when struck. The noise gradually gets less and less loud until it fades below the sensitivity of the human ear. The simplest model of how the gong produces the sound we hear treats the gong as a damped harmonic oscillator. The tone we hear is related...

Homework Statement "Which of the following applications would have the most benefit from a short damping time?" a. bathroom scale b. child jolly jumper c. suspension on passenger car d. suspension on race car Homework EquationsThe Attempt at a Solution Im assuming that both A and D should be...

I know the equation for damped oscillation where the damping force depends on velocity. In that case the damped oscillation has a fixed angular frequency and thus time period! I am wondering if there are any types of damped oscillation where the time period is not constant i.e. the motion is not...

I want to investigate the phenomenon of Chaos in the form of how its driving amplitude affects _____, in a driven, damped pendulum, using a computer simulation given. Initially I was looking at 'degree of chaos' for the dependent variable - to measure this I wanted to use the Lyapunov...

For an EM wave close to the transition frequency ##\omega_{21}##, we assume the dipole moment to be exponentially damped and oscillating: p(t) = p(0) e^{-\frac{\gamma}{2}t} cos(\omega_0 t) Why do we expect the electric field to be proportional to ##\dot p##? Taken from my lecturer notes on...

Homework Statement A forced damped oscilator of mass ##m## has a displacement varying with time of ##x=Asin(\omega t) ## The restive force is ## -bv##. For a driving frequency ##\omega## that is less than the natural frequency ## \omega_{0}##, sketch graphs of potential energy, kinetic energy...

Relevant equations 1) 2) T = \sqrt{ \frac{m}{k} } 3) T = \frac{2 \pi }{ \omega } In some problems about damped oscillatory motion, the requests ask for example "Calculate the amplitude after 20 oscillations" I know that i need to find the period first of all but : Do i find the period...

[Mentor's note: Thread title changed to reflect question content] I really need some help with this one: 1. Homework Statement An unhappy rodent of mass 0.307kg , moving on the end of a spring with force constant 2.48N/m , is acted on by a damping force Fx=−b⋅vx. Part A If the constant b has...

There is a post about the same problem here: https://www.physicsforums.com/threads/damped-oscilating-spring.12838/ It was helpful for solving part B. 1. Homework Statement A 10.6kg object oscillates at the end of a vertical spring that has a spring constant of 2.05x10^4 N/m. The effect of...

Homework Statement A block of mass m is attached to a spring of spring constant k. It lies on a floor with coefficient of friction μ. The spring is stretched by a length a and released. Find how many oscillations it takes for the block to come to rest. Homework Equations d2x/dt2 + k/m x = +_...

Relaxation time is defined as the time taken for mechanical energy to decay to 1/e of its original value. Why do we take a specific ratio of 1/e? What is its significance?

Homework Statement 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 displacement and speed as a function of the driving frequency and find the...

Homework Statement Solve u_{tt}(x,t)+2u_{t}(x,t)-u_{xx}(x,t)=18\sin\left(\dfrac{3\pi x}{l}\right) \omega=\frac{\pi n c}{l} Boundary conditions u(0,t)=u(l,t)=0 l<\pi Initial conditions u(x,0)=u_t(x,0)=0 Homework Equations [/B] The general inhomogeneous damped wave equation is u_{tt}(x,t)+2\mu...

Homework Statement A 4-pound weight stretches a spring 2 feet. The weight is released from rest 15 inches above the equilibrium position, and the resulting motion takes place in a medium offering a damping force numerically equal to 7/8 times the instantaneous velocity. Use the Laplace...

Homework Statement what is the energy loss of the damped oscillator. Homework Equations x(t) = A*e^(-Bt)*cos(w1*t) T = 1/2 mv^2 The Attempt at a Solution To solve for an undamped oscillator, I took the derivative of the equation of motion x(t) and plugged the amplitude into 1/2 mv^2 equation...

I've been researching on Damped Oscillation (in vibrations) for a few days for a research paper, however I couldn't find any applications. I would be very thankful if anyone can tell me about its applications.

Homework Statement Homework EquationsThe Attempt at a Solution For part (a) i did the following; the time for it to decay to 40% is half the period of the square wave = 0.00002 seconds So, 0.4qm = qm ## e^(\frac{-0.00002R}{2L})cos(25000*2*\pi*0.00002) ## But the cosine term yields -1 which...

Hello, I have two quick inquiries related to my studies on analytical mechanics. The first is I don't quite fathom how a full-width-half-maximum of the resonance of a forced and damped oscillator behaves in relation to the Q-factor?? And the second is does the amplitude of a forced and...