Driven oscillator Definition and 27 Threads

Here is the circuit as it appears in MIT OCW Vibrations and Waves Problem Solving course Here is my own picture I wrote equations for the three loops. Outer Loop Through ##C## $$-V_0\sin{\omega t}+IR+\frac{Q}{C}=0\tag{1}$$ Outer Look Through ##L## $$-V_0\sin{\omega...

The "Vibrations and Waves" problem-solving course on MIT OCW has a section on driven harmonic oscillators which can be seen here. I would like to do the first of the two problems. Unfortunately, there are two issues 1) The latex is not rendering on that website (relatively minor issue, I think...

I found ## \frac{\gamma}{2} = 7##, ##\gamma = 14## ##\omega_0^2 = \omega_d^2 + \frac{\gamma^2}{4} = 25## ##\omega_0 = \omega = 25##, thus ##\delta = \frac{\pi}{2}## ##A = \frac{\frac{F_0}{m}}{\sqrt((\omega_0^2 - \omega^2)+ \gamma^2\omega^2)} = 0.04## Thus, ##X(t) = 0.04sin(25t + \frac{\pi}{3} -...

My question also applies to the damped driven oscillator, however for simplicity I will first consider an undamped oscillator. The equation of motion is $$-kx + F_{0} \cos{\omega t} = m \ddot{x}$$ or in a more convenient form $$\ddot{x} + {\omega_{0}} ^{2}x = \frac{F_{0}}{m} \cos{\omega t}$$The...

I've seen the partition function calculated for the SHO before in a thermodynamics course in order to calculate entropy. Is it possible to calculate it for a driven harmonic oscillator?

So I've derived the equation for the amplitude of a driven oscillator as: \huge A=\frac{F}{m\sqrt{(\omega_{0}^{2}-\omega_{d}^{2})^{2}+4\gamma^{2}\omega_{d}^{2}}} Which is what my lecturer has written. Then taking the derivative and setting it to 0 to get the turning point. He makes this leap...

Description of the Problem: Consider a spring-mass system with spring constant ##k## and mass ##m##. Suppose I apply a force ##F_0 \cos(\omega t)## on the mass, but the frequency ##\omega## is very small, so small that it takes the system, say, a million years to reach a maximum and to go to 0...

Hello, in every book and on every website (e.g. here http://farside.ph.utexas.edu/teaching/315/Waves/node13.html) i found for driven harmonic osciallation the same solution for phase angle:θ=atan(ωb/(k−mω^2)) where ω is driven freq., m is mass, k is spring constant. I agree with it =it follows...

Homework Statement Homework Equations Complex number solutions z= z0eαt Energy equations and Q (Quality Factor) The Attempt at a Solution For this question, I followed my book's "general solution" for dampened harmonic motions, where z= z0eαt, and then you can solve for α and eventually...

Homework Statement I have a project in university that's about creating a simplified model of a washing machine in the program ADAMs View. Here is a picture of how it's constructed: https://imgur.com/a/zZzS5 So basically to oversimplify the problem I've understood that the rotating mass will...

Homework Statement An un-damped harmonic oscillator natural frequency ##\omega_0## is subjected to a driving force, $$F(t)=ame^{-bt}.$$ At time, ##t=0##, ##x=\dot{x}=0##. Find the equation of motion. Homework Equations ##F=m\ddot{x}## The Attempt at a Solution We have...

I started to ponder following problem. I have a driven, damped oscillator where the mass is free to vibrate in y-direction. If I put a wall or a ground near the mass, the mass touches it if the drive amplitude is larger than the distance to the ground. How does this change the normal dynamics. I...

http://depts.washington.edu/uwptms/research.html In a penning trap where they use sideband detection of the particle, they need to "drive" it. But what does that mean? Is the position of the particle detected anywhere along this process?

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 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...

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 Consider two masses m connected to each other and two walls by three springs with spring constant k. The left mass is subject to a driving force ## F_d\cos(2 \omega t) ## and the right to ## 2F_d\cos(2 \omega t) ## Homework Equations Writing out the coupled equations: $$...

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...

Hello Need some help simplifying this. In relation to a driven oscillator I am looking for wmax for which the amplitude is maximum. I understand the theory and I am just missing something with the maths and I know its probably something so stooooopid I am missing >< I'm taking the derivative...

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...

$$ -\sum_{n = 0}^{\infty}n^2\omega^2C_ne^{in\omega t} + 2\beta\sum_{n = 0}^{\infty}in\omega C_ne^{in\omega t} + \omega_0^2\sum_{n = 0}^{\infty}C_ne^{in\omega t} = \sum_{n = 0}^{\infty}f_ne^{in\omega t} $$ How can I justify removing the summations and solving for $C_n$? $$...

Homework Statement Consider a damped oscillator, with natural frequency ω_naut and damping constant both fixed, that is driven by a force F(t)=F_naut*cos(ωt). a) Find the rate P(t) at which F(t) does work and show that the average (P)avg over any number of complete cycles is mβω2A2. b)...

I found via this forum the hint to use the inverse squared equation to differentiate to find the resonance frequency from the amplitude equation (equilibrium not transient solution). Thank you! (AlephZero?) When substituting the resulting frequency for the resonance into the amplitude...

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...

Homework Statement http://fatcat.ftj.agh.edu.pl/~i7zebrow/rysunek.jpg tring constant is k, object mass is M_{1} Damping friction is b and we wiggle the top end of spring in the above diagram with amount Asin(wt) (Where A is a amplitude and w is a frequency). Homework Equations Spring...

Homework Statement "The equation mx'' + kx = F0 * Sin (wt) governs the motion of an undamped harmonic oscillator driven by a sinusoidal force of angular frequency w. Show that the steady-state solution is x = F0 * Sin (wt) /(m * (w0^2 - w^2)) Homework Equations x(t) = xta(t) +...

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...