Questions tagged [oscillators]

A mechanical or electronic system or device that works on the principles of oscillation, that is a periodic fluctuation between two things based on changes in energy. These range from abstract models such as a harmonic oscillator to electrical devices such as an LC circuit.

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Mysterious Action Optimization [closed]

I've been running some simple computational experiments to better understand the principle of stationary action, and have encountered some mysterious examples. Specifically, I'm running an ...
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How can I easily structure harmonic motion in a forces problem? [closed]

I have come across questions like the following which I need to be able to understand and model to get a differential equation: A particle, P, of mass $M$ is released from rest and moves along a ...
helpmewithmaffs's user avatar
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Rotating disc with viscous damping with large initial angle (always 90 degrees) (unbalance/instability)

I have an application for a rotating disc with inertia that is put on a "knife edge" balancing fixture. The disc is then released in order to find the "heavy spot", once identified ...
Mikro1234's user avatar
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Finding condition for Adiabaticity

I have a differential equation describing a resonator that looks like this: $$ \frac{d\alpha(t)}{dt} = [j a - b]\alpha(t) + \sqrt b e^{jct}$$ where I can solve it putting: $$\alpha(t) = \alpha e^{jct}$...
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Example of spring system modelled by $\ddot{x} + F(x,\dot{x}) \dot{x} + x = 0$, with given conditions on $F$

Consider the oscillator equation $$\ddot{x} + F(x,\dot{x}) \dot{x} + x = 0$$ where $F(x,\dot{x}) < 0$ if $r \leq a$ and $F(x,\dot{x}) > 0$ if $r \geq b$, where $r^2 = x^2 + \dot{x}^2$. What ...
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Is time period of a pendulum in an accelerating elevator dependent on the weight of the bob?

If a simple pendulum is in an elevator accelerating upwards, Its $T$ decreases. But why is that? The only thing that changes is the apparent weight so does $T$ depend on the weight of the bob but ...
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Lyapunov Exponent given two trajectories for a double pendulum [duplicate]

How can I calculate the maximal Lyapunov Exponent given two trajectories for a double pendulum? I have two trajectories (each containing two lists of $x$ and $y$ coordinates, for a small time step), ...
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Lyapunov Exponent for Double Pendulum

I want to calculate the Lyapunov Exponent for a double pendulum, with a small change in the initial angle. In this study, the authors used the formula $\frac{1}{t}{ln(\frac{d}{d_0})}$ as $t$ tends to ...
MaximeJaccon's user avatar
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EOM Double Pendulum with Mass of Rods

All the equation's of motion for a double pendulum do not include the masses of both rods. Is there an EOM for a double pendulum that takes into account the masses of the rods (not just the bobs)? Or, ...
MaximeJaccon's user avatar
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EOM for Double Pendulum using Newton's Laws of Motion

Whenever I've searched up the derivation of the EOM for the double pendulum, it has been done using the Lagrangian and generalized coordinates. Is there any method to get the EOM for the double ...
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Effect of gravitational time dilation on a classic weighted pendulum clock versus a hybrid pendulum clock with a battery

A classical pendulum clock is powered by gravitational potential energy by weights. While a hybrid pendulum clock is somehow propelled by electric current. Both have the same pendulum swing as the ...
Apsteronaldo's user avatar
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What really is oscillatory motion in physics? [duplicate]

Is it that oscillatory motion must be to-and-fro motion about a mean/stable equilibrium position, or it does not qualify as true oscillatory motion? Or, is it that most of the oscillatory motion has a ...
Krishna Sharma's user avatar
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2 answers
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Is bouncing ball (100% collision) an oscillatory motion/SHM or both or none?

My teacher told me bouncing ball (100% elastic) is oscillatory motion that does not have a stable equilibrium position and restoring force. It is just to and fro motion and thus called oscillatory ...
Krishna Sharma's user avatar
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Why is Simple Pendulum not SHM?

Why does Simple pendulum's motion not hold as SHM for large angles, only for small angle approximations? The restoring force is still directed towards the mean position. I know mathematically the ...
High School Student's user avatar
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Solving the decay $Q$ of transverse waves in a viscoelastic string based on this Kelvin-Voigt equation of motion?

Goal I am trying to solve a wave equation of motion for the transverse vibrations of a viscoelastic string fixed at each end to get the $Q$ (decay rate) of each harmonic (partial). The goal is to ...
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Modeling a viscoelastic string with a collection of damped spring oscillators? (To replace finite difference model.) How to find $Q$ per harmonic?

Background I have simulated a vibrating viscoelastic string fixed at each end under tension using finite difference modeling. Most simply this can be done using Kelvin-Voigt style mass-spring dampers ...
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Are there any "linear" lagrangian systems of interest for which an analytic solution is not obvious?

Out of curiosity, I am interested in Lagrangian dynamical systems that can be expressed in a "linear" manner. By this, I mean that their Lagrangian can be expressed, quadratically, as $$L = \...
Meclassic's user avatar
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Why sharp resonance corresponds to a particle?

First picture below is from last section of 23th chapter of Feynman's Lectures on physics. I don't understand the red line. This section talks about resonance in nature. It was very interesting and I ...
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Why is gravitational potential energy negative in this Lagrangian? [closed]

The question is given as follows: From (6.109) shouldn't the Lagrangian be K(kinetic) - U(potential), but here its K + U? Unless the potential energy is negative, if so I'm struggling to come to ...
orangesandjuice's user avatar
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Why the rope doesn't slack in the simple gravity pendulum?

One day I study the simple gravity pendulum, which an angle is less than $\frac {π}{2}$. It doesn't consider friction and air drag. In the simple gravity pendulum, My textbook says ”assume the rope ...
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Oscillation of Free End of String (Waves)

Suppose a wave pulse is produced in a string clamped at one end, and the other end is loose(tied with a massless ring which can move along a vertical rod, there's no friction). Now, I have searched ...
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Do these two systems of differential equations both describe the motion of the elastic pendulum?

The elastic pendulum is a chaotic dynamical system which is equivalent to a mass attached to a string in 2 or 3 dimensions. It exhibits complex harmonic motion and chaotic behavior. Wikipedia gives a ...
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What shape will two independent pendulums draw?

At an art exhibition I saw a piece that looks like this: There are two independent rod pendulums each with an equal mass $m$ at the end. One pendulum has a blank piece of paper attached to it. The ...
operator's user avatar
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Full Expression for energy in damped harmonic oscillator [closed]

The equation of motion for a damped harmonic oscillator is $$m \ddot{x}=-sx-r\dot{x}$$ where $s$ is Hooke's constant and $r$ is damping coefficient. For Damped Harmonic motion, $$x=Ae^{-pt}(\sin(wt+l))...
GedankenExperimentalist's user avatar
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Critical damping and mathematical requirement of 2 constants

The general equation of an oscillator with a damping term $-rv$, where $r$ is damping coeffeciet and $v$ is velocity is $$x=e^{-pt}(Ae^{qt}+Be^{-qt})$$ where $p=r/2m$ and $q=\sqrt{p^2-s/m}$, $s$ is ...
GedankenExperimentalist's user avatar
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2 answers
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Why, when determining the lengths of pendulums for a pendulum wave, do you use the equation $L = g[Tmax/2π(k+n+1)]^2$?

Why, when determining the lengths of pendulums for a pendulum wave, do you use the equation $L = g[Tmax/2π(k+n+1)]^2$?
Lucien Jaccon's user avatar
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Particle in an oscillating box [closed]

This isn't a question for a class, it's just driven by curiosity. I hope you like it. Let's consider a particle in a box with infinite potential barriers, but now the walls can oscillate/move. Does ...
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Why actually at resonance the inductive and capacitive reactance cancel each other?

I am learning about series LC circuit that is in resonance. It says it is when the impedance offered is minimum due to the angular frequency being at a particular value(1/√LC).People say that they are ...
Dhyaneshwar's user avatar
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Normal modes of three masses attached by two springs

I have the following system: I've applied Newton's 2nd Law to the system and I have found the normal modes proceeding as an eigenvalues and eigenvectors problem. I obtained the frequencies $\omega_1^...
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Procession in Pendulum Art

https://www.youtube.com/shorts/Kgs9_3UH3Pk In this video, a pendulum is formed from a paint can full of paint with a hole in the bottom. The pendulum's swing traces out an ellipse that slowly rotates ...
DinoFeet's user avatar
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What's the actuating force on a spring?

I'm trying to solve the following problem: a) Consider a spring (of constant $K$) fixed on one end, $F_1$ is applied on the other such that $x=x_0\ cos(\omega t)$. What does $F_1$ have to be? b) A ...
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Frequency Response of a Stochastic Oscillator Numerically

I am willing to obtain a frequency response plot for a stochastic oscillator governed by the following equation numerically. $$ \ddot{x}+2\Gamma \dot{x}+\omega_{0}^{2}x=f(t) $$ where $f(t)$ is a ...
Sourin Dey's user avatar
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Asymmetry when $t\rightarrow -t$ [duplicate]

If we consider the equation of critical damping $$x=(a+bt)e^{-ct}$$ then the graph is However, it is asymmetric for positive and negative time values. I have an intuition that this should be the case ...
GedankenExperimentalist's user avatar
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Critical damping: second solution of oscillator differential equation with pertubation

With critical damping, when you look at the characteristic polynomial you have a double root instead of two distinct roots, but there must nonetheless be two separate solutions to the differential ...
16π Cent's user avatar
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How can one explain the small amplitude resonance before the onset of main resonance condition?

I was using a sonometer to verify the frequency of a.c. supply in the lab is 50 Hz. For this the equation I used is f=(1/4L) x Sq. root (T/m) I set tension T = 4.9 N by hanging 0.5kg mass mass per ...
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Oscillator with non-linear damping - question re a specific approach

The following paper https://core.ac.uk/reader/82037870 Oscillators with nonlinear elastic and damping forces L.Cveticanin studies the general problem $$ \ddot{x} + 2 b_k \, \dot{x} \, |\dot{x}|^k + \...
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Is sound essentially motion?

From my understanding, the only way for humans to create sound is by moving our bodies, vocal cords, or by moving other objects. So depending on how fast we or other objects can move, different ...
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Oscillator with non-linear damping / drag equation

For linear damping $$ \ddot{y} + 2\beta_0 \, \dot{y} + \omega_0^2 y = 0 $$ the solution with initial conditions $y(0) = y_0, \; \dot{y}(0) = 0$ reads $$ y(t) = y_0 \, \sec\delta \, e^{-\beta_0 t} \, \...
TomS's user avatar
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Is projection of a simple pendulum, doing SHM as well?

I know projection/shadow of a Uniform Cirular Motion does SHM, and a simple pendulum also does shm. But I was wondering whether, for a pendulum in $xy$ plane having its central axis parallel to $y$ ...
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Numerically determining steady state in oscillating systems

As the title says, I'm trying to determine numerically when an n-DOF oscillating system (linear or nonlinear) subjected to forced base oscillation reaches the steady state solution. Is there an energy ...
DanMacBen's user avatar
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1 answer
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Force-dependency of frequency response of driven harmonic oscillator with damping

For a driven harmonic oscillator with damping of the form \begin{equation} \ddot{x} + 2\xi\omega_0\dot{x} + \omega_0^2x = \frac{F_0}{m}cos(wt) \end{equation} with damping ratio $\xi$ and natural ...
Merkel_Bot's user avatar
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Approximate Solution to Damped Nonlinear Pendulum

The Nonlinear Damped Pendulum Equation $\ddot{\theta}+\frac{b}{m}\dot{\theta}+\frac{g}{l}\sin(\theta)=0$ isn’t exactly solvable unlike the Nonlinear Pendulum as there’s no constant of motion namely ...
Masteralien's user avatar
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The frequency is off by a factor of $2 \pi$?

I was reading Morin's Introduction to Mechanics, and the following material came up: At equilibrium point $x_0$ expanding the Taylor series, we see $V(x)=\frac12 V''(x_0)(x-x_0)^2$ so comparing this ...
Aditya_math's user avatar
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Solutions to critically damped harmonic oscillator?

From MITOpenCourseWare, I was learning about the damped harmonic oscillator. Some context is pasted below. Case (iii) Critical Damping (repeated real roots) If $b^2 = 4mk$ then the term under the ...
Arden Tsang's user avatar
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Steady-state of an expectation value of an oscillator system

For context, I am dealing with an equation of motion for the expectation value $\beta=\left\langle\hat{b}\right\rangle$ of a quantum van der Pol oscillator. But I would love a more general explanation....
Len's user avatar
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In a damped oscillation with damping force $F=-bu$ at which position does the maximum velocity occur?

In a SHO we know that V will become a maximum in the equilibrium position with V= Aω. Does the same apply to a damped oscillation with the damping force being F=-bu or is the position somewhere else?
justcurious's user avatar
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1 answer
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Show that $dE/dt = -bv^2$ (Help with differentiation) [closed]

The question is: Show that $$dE/dt = -b (dx/dt)^2.$$ And the solution is: ...
Theo's user avatar
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Analytic description of oscillations in a rotating frame of reference?

Imagine you have a pendulum attached to a rotating axis. You define two frames of reference. In the $S$ frame, the pendulum is oscilating and rotating around this axis. The $S'$ frame is define such ...
Álvaro Rodrigo's user avatar
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Does rhythm create pitch?

As in, matter (a physical object) that is vibrating = a pitch And secondly If we calculate bpm with a “tick” which is just indefinite pitched percussion, how does an indefinite pitched beat compare to ...
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Natural Harmonics on a String

Consider the Dirichlet boundary value problem of a guitar string stretched between two fixed points which is made to oscillate by pinching and releasing the string. It can be shown in quite ...
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