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61 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 ...
2
votes
1answer
63 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 $a$, ...
5
votes
2answers
814 views

Pendulum period [duplicate]

In plane pendulum problem, we can calculate its period using elliptic integration. In SHO problem, we use approximation such that $\theta\ll 1$ and get the period, $2\pi\sqrt{l/g}$. Is there another ...
0
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0answers
2k views

What is the difference between Non-harmonic oscillation, Anharmonic oscillation and Complex harmonic oscillation?

I am just wondering if the words Non-harmonic oscillation, Anharmonic oscillation and Complex harmonic oscillation mean the same thing. If not what exactly is the difference between them? Since the ...
-1
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1answer
314 views

Simple pendulm motion for larger angular displacement? [duplicate]

What will be the nature of the motion of a simple pendulum for larger angular displacement? Will that be a periodic motion? If so, will the time period increase or decrease?
0
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2answers
280 views

Can there exist harmonic oscillator with asymmetric coupling?

In Classical Mechanics textbooks usually, for a coupled harmonic oscillator with two masses, coupling is taken to be same in both directions (i.e coupling constant w.r.t to m1 is same as that with ...
26
votes
3answers
5k views

Why does a simple pendulum or a spring-mass system show simple harmonic motion only for small amplitudes?

I've been taught that in a simple pendulum, for small $x$, $\sin x \approx x$. We then derive the formula for the time period of the pendulum. But I still don't understand the Physics behind it. Also, ...
0
votes
1answer
352 views

The actual period of a pendulum at 90°. Looking for the correct formula

Do you have access to any scientific experiment which gives the period of a pendulum when the angle is $90^\circ$: this article says $T$ varies to about $18\%$ up to $90^\circ,$ so for a seconds ...
0
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0answers
297 views

Anharmonic oscillator on quantum mechanics

I'm studying the following Hamiltonian for an anharmonic oscillator in quantum mechanics: \begin{equation} \hat{H} = \frac{1}{2 m} \left( \hat{\vec{p}} - \frac{e}{c} \hat{\vec{A}} \right) + \frac{ m \...
1
vote
1answer
103 views

Pendulum motion equation issue

The differential equation that gives the equation of motion of a pendulum where: $m$ is the mass $L$ is the distance between the pivot and the body's centre of mass $g$ is the acceleration due to ...
3
votes
0answers
669 views

What is the mechanism of subharmonic oscillations?

It's clear to me from linear systems theory that energy manifested within a fundamental mode of resonance can saturate with the excess energy spilling over into harmonic frequencies greater than the ...
0
votes
1answer
791 views

Does sound absorption depends upon the amplitude of sound wave?

I can understand the mechanism of frequency dependant sound absorption by most materials but does the sound attenuation also depends upon the AMPLITUDE(sound pressure or rather loudness/sound ...
1
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1answer
1k views

Anharmonic oscillator solution function

I am solving a CLASSICAL an-harmonic oscillator problem with Hamiltonian given by $$H= (1/2)\dot{x}^2+(1/2)x^2-(1/2)x^4$$ with all the constants ($k$'s) and mass being taken as 1 (one). I find that $...
3
votes
2answers
1k views

Period $T$ of oscillation with cubic force function

How would I find the period of an oscillator with the following force equation? $$F(x)=-cx^3$$ I've already found the potential energy equation by integrating over distance: $$U(x)={cx^4 \over 4}.$$...