Questions tagged [oscillators]

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101 views

Doubt in quantum mechanics [on hold]

My lecturer said that when a oscillating body loses energy in the form of radiation the natural frequency of oscillation is equal to the frequency of the emitted radiation. Can someone explain why?
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0answers
15 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
47 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
27 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
41 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
28 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
36 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
22 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
44 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 ...
2
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1answer
43 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 ...
5
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2answers
111 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
67 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
32 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
142 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
39 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
44 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
27 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
69 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
89 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
49 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
112 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
19 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
39 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) ...
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1answer
34 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
30 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
91 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
74 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
111 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
69 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
51 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
206 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
48 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 ...
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1answer
64 views

Time period of an oscillatory motion [closed]

The question: A particle of mass $m$ is executing oscillation on the $x$-axis. Its potential energy is $U(x)= K|x|^3$, where $K$ is a positive constant. If the amplitude of oscillations is $a$, ...
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2answers
185 views

Why the time period of pendulum with infinite length is $84.6$ minutes? [closed]

In a book I was reading about SHM it stated: If the length of a simple pendulum is increased to such an extent that $\ell\to\infty$, then its time period is given by, $$T=2\pi\sqrt\frac{R}{g}\...
3
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1answer
51 views

Pendulum in a Boat [closed]

Suppose a pendulum is kept in a boat and it is oscillating. Now if the boat is made to oscillate in the same direction or opposite to that of the pendulum, how will these affect the amplitude of the ...
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5answers
2k views

How can I prove that a state of equilibrium is unstable?

In the particular problem I encountered, an electric field was zero at the origin and we were meant to prove that a particle at the origin was in an unstable state of equilibrium. Is it enough to ...
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3answers
90 views

Potential energy of an oscillating pendulum

The following question always confuses me. for an oscillating pendulum why the potential energy is given by: $$V = mgL(1-\cos\theta)$$ Why not $$V = mgL\cos\theta$$ Is this a convention or there ...
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0answers
61 views

How long does it take for a wave pulse on a string to get reflected from rigid boundary?

This question arises from analysis of standing waves.The incident wave has the equation $$y=Asin(kx-\omega t)$$The reflected wave has the equation$$y=Asin(kx+\omega t +\pi)$$When determining the ...
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3answers
53 views

Inserting an arbitrary phase in the equation for driven damped oscillations

In Classical Mechanics by Taylor, we find the solution to the differential equation of a damped oscillator with a sinusoidal driving force: $$\ddot{x} + 2\beta\dot{x} + \omega_0^2x = f_0\cos\left(\...
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1answer
63 views

Is energy conserved in a Van der Pol oscillator?

The Van der Pol Oscillator is governed by a 2nd order ODE with nonlinear damping. The 'position' of the oscillator is the solution to $$x''(t) = \mu (1 - x^2(t)) x'(t) - x(t)$$ Here $\mu$ controls ...
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1answer
48 views

What does the viscous damping coefficient depend on?

I’m doing a theoretical calculation involving the damping on an oscillating string, and I found the following relationship, where a certain damping factor $b$ is proportional to $\frac{c}{d^2}$ where $...
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0answers
54 views

Prove from first principles that a guitar string will vibrate at a constant frequency

From experience I am aware that a taught string will generally vibrate with a constant frequency. I wanted to prove this by considering the relation of distance from the resting position, and its ...
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1answer
73 views

What is complex frequency? [closed]

I am learning EE, and about complex frequencies, but what is its physical meaning? What is it used for? Why is it? And only happen in the laplace transform?
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1answer
232 views

Difference between simple harmonic motion and angular SHM

I am not able to decipher when it is simple harmonic motion and when it is angular harmonic motion. Can we use both of them interchangeably? Can I know all the variable analogous for angular SHM (by ...
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1answer
36 views

Oscillations - Mass Change on Simple Pendulum

The problem that I am thinking of is phrased as follows: A person on a swing is holding a sandbag and is moving with some initial velocity $v_0$ at the bottom of the swing of length $l$. The ...
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4answers
89 views

Solutions to Newton's laws with unbounded kinetic energy for inverted harmonic oscillator potential

In a one dimensional setting, Hooke's Law, together with Newton's 2nd law, results in a differential equation of the form (setting the constants $m$ and $k$ equal to 1 for notational simplicity) $x''(...
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1answer
40 views

Could the flex in a skyscraper due to wind be used to produce power?

While browsing 'Hot Questions' on Stack Exchange I came across this question: Can we use the stored gravitational potential energy of a building to produce power? It got me thinking about the use of ...