Questions tagged [oscillators]

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$Q$-factor of oscillator

Given the equation for a damped oscillator is $$\ddot{x}+\gamma\dot{x}+\omega_0^2x=0$$ Is the $Q$ factor of the system given by $\omega_0/\gamma$ or $\omega_0/2\gamma$? I have seen both forms come ...
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35 views

Damped Forced Oscillator with initial conditions

The equation of motion of a damped forced oscillator is; $$\ddot{x}(t)+\gamma\dot{x}(t)+\omega_0^2x(t)=F(t),$$ $$F(t) = F_0 \cos(\omega_dt);$$ also for the purpose of this problem we may set $\...
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38 views

Pendulum: Time period for effective length varying with angle

For a pendulum whose effective length changes with angle, my approach would be to write the length as a function of the angle: $\ell(\theta)$, then using the torque derivation of the time period I do ...
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2answers
29 views

Does the length variable in pendulum motion include center of mass?

In diagrams, is the bob/mass of the pendulum considered a point, or a 2/3D object? And furthermore, is the length variable in the period of a pendulum simply the length of the string, or is it really ...
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25 views

Elongation of a simple pendulum

One of the questions on this weeks question sheet asks for the maximum elongation of a simple pendulum. The pendulum is set in motion on the moon with f = 0.5Hz. What is meant by the elongation of the ...
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0answers
16 views

Effect of external forces on a horizontal mass dampener

I am reading this paper which models the motion of a horizontal mass dampener. They say that on adding a dampener, the equation consisting of the forces is: $ma = -cv -kx$ where $ c$ = damping ...
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23 views

Dynamics problem related to harmonic motion

I am unable to proceed further , the particle in this is falling with variable acceleration Fy toward origin with its greatest and least values given of the function is given, please explain where ...
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3answers
42 views

Does resonance just depends upon the frequency of the external periodic force and the natural frequency of an object?

I am a little confused about the phenomenon of resonance, I read that it occurs when the frequency of an external force matches the natural frequency of an object. So, it was given that soldiers ...
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1answer
43 views

$Q$ factor of a pendulum

according to the definition of the Q-factor of damping, it is given by: $Q = 2\pi\frac{Energy \; Stored}{ Energy \;Dissipated \; per \;cycle }$ Q = 1⁄2 --> Critical damping Q > ​1⁄2 --> Over ...
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0answers
40 views

External force in the Navier-Stokes momentum equation

The Navier-Stokes momentum equation is $$ \rho\frac{\partial \bf{v}}{\partial t}+\rho(\bf{v} \cdot \nabla\bf{v})=-\nabla P + \nabla\cdot \bf{\tau} +\bf f $$ where $\tau$ is the deviatoric stress ...
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0answers
33 views

Why is water in the asymmetric cylinder not capable of Simple Harmonic Motion?

I'm learning physics in a high school. I'm curious why water in the asymmetric cylinder is not capable of SHM. I've learned that water in a symmetric cylinder can make a Simple Harmonic Motion. But ...
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1answer
68 views

Solution of a differential equation in physics

In physics when we solve the differential equation, in some cases we get two part of the solution, one is real and another is imaginary. Some cases we consider that the real part have some physical ...
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23 views

Incorporating matter effects on active-sterile neutrino oscillation with mathematica

I recently wanted to study the effect of a constant matter potential on a simple 2-flavor active-sterile neutrino oscillation system using Wolfram Mathematica, but I encountered a big problem in the ...
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2answers
60 views

What's wrong with my approach?

Let's say you have a pendulum moving in SHM with a length $L$ and an amplitude $\theta$. Suppose you wanted to find the linear velocity $v$ at it's lowest point. The way that gets the right answer ...
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5answers
150 views

Wave Equation derivation

I'm curious about part of the derivation of the wave equation as is done in all references that I've seen so far (I'm gonna reproduce only the part that's puzzling me). We apply Newton's second law ...
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0answers
25 views

Magnet oscillation with coils

I am trying to conduct an experiment in which I will try to find the natural frequency of a cantilever. To oscillate the cantilever, I thought I could use a magnet and a current-carrying coil wire ...
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0answers
17 views

How can I calculate magnetic field strength of a variable gap magnet?

I am currently doing an experiment where an aluminium pendulum is passed through a variable gap magnet (creating eddy currents). The variable I am changing is distance between the two grade N35 ...
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0answers
56 views

If a hollow sphere connected to a rope and half-filled with water forms a physical pendulum, what does the water surface do?

Suppose I make a pendulum consisting of a long string connected to a hollow sphere, then fill the sphere half way with water and set the pendulum in motion by giving all the water and the sphere some ...
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1answer
28 views

Minimal dynamical system with quasiperiodic oscillations

What is a minimal, explicit dynamical system (as in, a series of coupled ordinary differential equations) that exhibits quasiperiodic oscillations for some region of parameter space? Two coupled Van ...
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2answers
43 views

Can I discover the intial length/dimensions of spring from $mx''+cx'+kx=0$? [closed]

Can I discover the intial length/dimensions of spring from $mx''+cx'+kx=0$? This (by solving with e.g. RK4) allows me to simulate the motion of the object tied to the spring or the "spring head". ...
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1answer
29 views

What's the “cause” of damping coeff. in springs?

What's the "cause" of damping coeff. in springs? Air resistance, friction?
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0answers
43 views

Analytical solution to damped harmonic oscillator - Fokker-Planck equation

In the paper "Numerical solution of two dimensional Fokker-Planck equations" (available at: https://doi.org/10.1016/S0096-3003(97)10161-8), the authors quote an analytical solution to the damped ...
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0answers
39 views

Calculate viscous damping coefficient given force

With a force metre I recorded the force vs time of a spring with a disk on the end in water, experiencing viscous damping, during damped oscillatory motion. I pulled the disk to the bottom of the ...
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0answers
48 views

3D harmonic oscillator magic numbers

I know that, $$V(r) = (1/2) m \omega^2 r^2 ,$$ $$\omega \approx 40(Z+N)^{-1/3}\ \rm{MeV} $$ and $$E = (n+3/2) \hbar \omega.$$ How do you find the magic numbers of protons and neutrons which ...
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1answer
68 views

Sonority of metals [closed]

Is there any reasonable atomic theory which can provide a rational reason for the existence of sonority in metals? Almost all the non-metals do not exhibit sonority. Can it be correlated to the ...
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2answers
115 views

Why are sinusoids so common in nature? [duplicate]

When we are introduced to waves in school, we are often presented with a picture of a sinusoid (or a cosinusoid). Sinusoids can represent the way many physics phenomena behave, still.... Why are ...
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1answer
93 views

How is a quartic oscillator solved in classical mechanics?

Quantum mechanically, a quartic anharmonic oscillator with potential $$V(x)=\frac{1}{2}m\omega^2x^2+\lambda x^4$$ is dealt with perturbation theory- the approximate energies $E_n$ and energy ...
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1answer
33 views

Damped harmonic oscillator's maximum displacement [closed]

I want to know the maximum displacement $x_0$ of a mass $m$ on a spring with spring constant $k$, in the case that the system is damped with damping constant $c$, and where the initial velocity $v_0$ (...
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2answers
386 views

Difference between Oscillatory motion and vibratory motion

What is the difference between oscillatory motion and vibratory motion. I have read in my book that "If the amplitude of oscillatory motion is extremely small,the motion is called vibratory motion". ...
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0answers
44 views

Resonance and energy flow

In this post, Alfred Centauri describes the resonance as a phenomenon which appears when 'the energy flow from the driving source is unidirectional' and then shows that this is the case for $\Omega=\...
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1answer
48 views

Damped forced Oscillation with variable external frequency

Consider that we have the following forced vibration with an input frequency $ω(t)$ variable in time. $$m\ddot{x}+c\dot{x}+kx = F_0 \sin{(\omega(t) t)}$$ Assuming that the solution must be a ...
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0answers
30 views

Spring oscillation model

When a spring - in real world - is extended $Xo$ from its natural position, it oscillates and eventually decreasing it's amplitude with time, comes to a stop. Is this a damped system or no? If yes how ...
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1answer
106 views

What is the difference between reciprocating and oscillating motion? How is reciprocating motion different from simple harmonic motion?

I wanted a good explanation for the difference between reciprocation and sinusoidal motion (For e.g. SHM). This question has been posted here due to many ambiguous and unclear explanations round the ...
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1answer
104 views

Modification of the Verlet algorithms for the pendulum problem

I'm trying to write a program to integrate the motion equations of the pendulum in the damped and forced case, that is, following this equation: $$ \frac{d^2\theta}{dt^2}=-\frac{g}{L}\sin(\theta)-\mu\...
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0answers
10 views

Frequency of the Primary Circuit in a Spark Gap Tesla Coil

In a simple spark gap tesla coil, how does the oscillating current in the primary circuit interact with the supply voltage/current? If the power supply comes from a transformer hooked up to the ac ...
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0answers
54 views

How to evaluate the period of a particle in a system with potential energy $U=-U_0/\cosh^2(\alpha x)$?

I am working through the textbook "Mechanics", from the series "Course of Theoretical Physics " by Landau and Lifshitz. In Chapter 3, where the authors talk about integrating the equation of motion $E=...
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1answer
142 views

How can dissipative/friction terms be incorporated into a Lagrangian?

I'm trying to find a suitable Lagrangian for a damped harmonic oscillator, a system that satisfies the following equation of motion: $$m \ddot{x} + \gamma \dot{x} + \frac{d\phi}{dx} = 0.$$ What I ...
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0answers
24 views

String conservation with springs

I was trying to solve this Problem that asked to find the period of small oscillations for this system. To do so I used the fact that for a massless pulley with strings around it, the sum of the ...
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1answer
40 views

Tone production in Irish Flutes?

Since it's about a technical issue, I thought that this question would fit in here the best (as opposed to the music.stackexchange-site): I'd like to know how tone-production in an irish (wooden) ...
2
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1answer
35 views

Electron equations of motion for plasma

I'm reading through an Introduction to Plasma Physics by Francis F. Chen, and in the simplified derivation for plasma oscillation in 1D, the book quotes the electron equations of motion as: $$mn_e\...
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1answer
32 views

1D string reflection and transmission phase

Ok, I must be missing something very obvious here. After applying the boundary conditions, we can write: $$ A_R e^{i \delta_R} = (\frac{v_2 - v_1}{v_1 + v_2}) A_I e^{i \delta_I} $$ and $$ A_T e^{...
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1answer
94 views

Quantum Theory: Why Particles Oscillate? [closed]

I understand that as the energy of a particle increases, it oscilates more visciously. I know that there isn’t a consensus on this, but are there any theories out there that explain what causes ...
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1answer
75 views

Estimate pendulum motion

I have a simple system: a pendulum and two sensors (RADAR which will tell the distance $dx$ and $v_x$ and a Gyroscope, the gyroscope is giving me the information about $\omega$ - angular velocity) as ...
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1answer
115 views

Oscillation of Chocolate bar on soda [closed]

Why does a piece of chocolate bar oscillate in soda (i.e. floats then after a while sinks and vice versa)? What parameters does the period of oscillation rely on? Is there a specific formula that ...
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3answers
88 views

Rotational Kinetic Energy of a Pendulum

By the parallel axis theorem, a pendulum that rotates around a point $P$ and a distance $l$ from it's center, has kinetic energy $E_{kin}= \frac{\omega^2}{2}(\frac{2mR^2}{5}+ml^2)$. Where R is the ...
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0answers
35 views

Why a musical instrument's string oscillates with many frequencies? [duplicate]

I am trying to understand why when we play a note on a stringed instrument, not only it oscillates with it's fundamental frequency but also the multiples of that. For instance if you play a D on the ...
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1answer
69 views

Effect of elasticity of string on simple pendulum

In a simple pendulum system, how does the extensibility/elasticity of the string affect the time period of oscillation? Would it lead to a random or systematic error? Would the elasticity of the ...
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6answers
1k views

Springs with some finite mass

Let us consider a spring which is having some finite mass. By the help of some external agent the spring has been extended by some distance $x$. Will the restoring force produced in the spring still ...
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2answers
270 views

When you increase the tension on a string, how is the standing wave affected?

I know that wave velocity is the product of wavelength and frequency, and that velocity is proportional to string tension. Does this mean that if you increase the tension on a string, the wavelength, ...
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2answers
57 views

Does damping force depend on frame of reference?

I learn that damping force with regard to forced damped oscillations is given by F = -bv where is the velocity of the object measured from ground frame. Suppose we are in a frame which is moving with ...