The term "harmonic oscillator" is used to describe any system with a "linear" restoring force that tends to return the system to a equilibrium state. There is both a classical harmonic oscillator and a quantum harmonic oscillator. Both are used to as toy problems that describe many physical systems.

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Is it possible to derive the angular frequency of a simple harmonic oscillator using total energy?

I want to show that $$\omega=\sqrt{\frac{k}{m}}$$ using the fact that $$E=K+U=\frac{1}{2}mv_x^2+\frac{1}{2}kx^2=\frac{1}{2}kA^2.$$ The issue is that I have derived a formula that isn't ...
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28 views

Position, Velocity and Acceleration in a Forced Harmonic Oscillator [on hold]

The problem is the following: An particle has a potential energy enough so that the 0.2Kg particle moves up 0.45m and has a displacement of 1.78m. The particle presents a period of 0.1242s, and is ...
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29 views

Finding the motion of an object on a spring given its mass and displacement [closed]

A mass of $500gm$ is suspended from the ceiling by a frictionless spring, it stretches the spring $50cm$ before getting to its equilibrium position, where the mass pulling down is balanced exactly by ...
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59 views

amplitude of two carts attached by a spring [closed]

The problem statement: All variables and given/known data [Coupled Oscillators] A cart of mass $m$ (car #1) and another cart of mass $2m$ (car #2) on a horizontal surface are connected by an ideal ...
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34 views

Using creation and annihilation operators to prove the expression for the $n$th excited state in terms of the vacuum state

How does one prove that the $n^{th}$ excited state of a quantum harmonic oscillator (QHO) can be obtained by applying the creation operator $a^{\dagger}$ $n$-times to the vacuum state $\vert ...
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71 views

Has anyone published the procedure to generalize ladder operators for any potential in Schrodinger's equation?

I know that the ladder operator for the quantum harmonic oscillator \begin{align} H\psi_m = \left(\dfrac{p^2}{2m}+\dfrac{1}{2}m\omega^2x^2\right)\psi_m=E_m\psi_m \end{align} is \begin{align} A = ...
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1answer
35 views

Can an object experience torque when the only applied external force is at its axis of rotation (IOW, where $F \times r = 0$)?

This question came up because of this diagram that I saw in my textbook of an angular simple harmonic oscillator. I've always struggled a bit with torque and rotational dynamics in general, and I ...
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487 views

Is the usually taught solution to forced harmonic motion just a special solution?

Let's say we have a mass on a spring being driven by a forcing function. Given hook's law, $F = -kx$, and a forcing function of $$F(t) = F_0\sin(\omega t) .$$ We can write: $$ m\frac{d^2x}{dt^2} = ...
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23 views

Reflection of Sound wave (Pressure Wave)

I want to study about the phenomenon of reflection of pressure waves as in an open ended organ pipe. Please suggest a suitable resource? I know about the harmonics in a stretched string and I can use ...
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44 views

discrepancy in theoretical and natural frequency?

In an experiment to determine the natural frequency of a spring-mass-pulley system, why would the experimental natural frequency (found using 1/time) be greater than the theoretical natural frequency ...
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1answer
16 views

Can the logarithmic decrement be found from extension of spring?

Consider a spring-mass system in which a mass hangs freely from a spring fixed to a ceiling. Can the logarithmic decrement be found simply from the extension of the spring? The only parameters known ...
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1answer
34 views

Problem about a spring which oscillates due to a external force [closed]

A person holds a spring of stiffness $k= 80$ N/m by its extremity A; In the other end there is a mass of $0.5$ kg. The spring is initially at equilibrium, when the person starts to shake the ...
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1answer
62 views

Meaning of “vacuum state”?

I just learned about $|0\rangle$ and siblings $|0_\gamma\rangle$ and $|0_\infty\rangle$ while studying coherent and squeezed states in a QM class, and I have a question about the meaning of ...
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19 views

Effect on Q factor and resonant frequency when scaling down a damped oscillator to micro / nano scales

I've always just accepted that as you scale down a mechanical system the frequency and Q factor both increase. But how exactly do they scale? Linearly? With the square of reduction in size? Or maybe ...
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2answers
33 views

Acceleration of Simple pendulum [closed]

A simple pendulum starts its motion from one extreme when it left at extreme it starts its motion towards the extreme and its velocity become increase and become maximum at mean position and also ...
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1answer
28 views

Quantum harmonic ocillator and the mean energy U(T)

The energy of a quantum harmonic oscillator is given by: $$E(n)=\hbar\omega\left(n+\frac{1}{2}\right)$$ The canonical partition function is given by: $$Z(T)=\sum_{n=o}^\infty e^{-\beta ...
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37 views

How to calculate the resultant movement of a superposition of harmonic oscillators?

If $x_{1}(t) = \cos(\omega t - \frac{\pi}{6})$ and $x_{2}(t) = \sin(\omega t)$ are two simple harmonic oscillators in the same direction and with the same angular frequency $\omega$, how to ...
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1answer
20 views

Mass-Spring system on an accelerating jet

Imagine a perfect mass spring system. If it's put on an accelerating plane, how will the motion change? Is the plane's acceleration like a driving/damping force, where: $$F_{\text{driving}} = ...
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1answer
71 views

Finding time period of oscillations in a multiple spring system attached to a solid cylinder [closed]

A solid cylinder of mass $m$ and radius $R$ is kept in equilibrium on horizontal rough surface. Three unstretched springs of spring constant $k$, $2k$, $3k$ are attached to cylinder as shown in the ...
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50 views

Two masses on a frictionless surface connected with a spring

I have a problem with an assignment with two masses on a frictionless plane connected with a spring. Both masses are 1 kg, and the distance between them (the length of the spring) is 0.4 m. The ...
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42 views

Amplitude-Frequency curve

Given a resonance curve just like this: Could someone explain to me what the physical meaning of the intersection with the ordinate is? At first glance I would say it has to be $(0 | 0) $ since ...
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58 views

Can a body execute two Simple Harmonic Motions instantaneously?

If we use a helical spring instead of string in a simple pendulum then will the body execute two simple harmonic motions simultaneously? Like up-down motion of spring and to and fro motion of simple ...
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1answer
48 views

Derive Equation For a Cantilever in SHM

I am currently investigating how a hacksaw blade's time period of oscillation changes when I add mass to the end of it or when I change the length it is clamped at. I found the following equation ...
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1answer
40 views

Average Energy of a coherent state

The question is relating to a previous problem concerning the harmonic oscillator. Determine the average energy < E > in a coherent state |alpha>. From my understanding the expectation of the ...
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129 views

Please explain the following graphs that describe a quantum mechanical harmonic oscillator

Graphs such as the above keep coming up when talking about harmonic oscillators in a quantum mechanical sense. However, I simply cannot make sense of them. What does each line represent why are they ...
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Forces acting on an SHM

I would like to know the forces acting on an SHM, and how they effect the motion. For example, take the motion of a simple pendulum as in the given image. Which are the forces acting on this motion? ...
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62 views

How to determinate the minimum period of oscillation for a physical pendulum? [closed]

A physical pendulum consists of a thin homogeneous rod of length $l$, suspended by a point $O$ at a distance $x$ from the center of gravity ($x<\frac{l}{2}$), oscillating in a vertical plane. ...
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1answer
48 views

What is the relationship between harmonic motion and the harmonics of a wave?

I learned about harmonic motion and harmonic oscillators a long time ago in physics, but I can't remember what the relationship between that and and the definition of harmonic in a wave. A harmonic ...
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55 views

Computing $\langle0|T[Q(t_2)Q(t_1)]|0\rangle$

Given Hamiltonian $H=\frac{P^2}{2}+\frac{\omega^2}{2}Q^2$, compute $\langle0|T[Q(t_2)Q(t_1)]|0\rangle$, where $T$ is the time-ordering of the product, $|0\rangle$ is the ground state. Now set ...
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25 views

Is there a curve for which a particle restricted to move within it under the gravitational force will always exhibit a pure harmonic motion?

A simple pendulum, for example, is not isochronous for large amplitudes (that is, the frequency will depend on the amplitude). So a particle confined in a circumference will not always exhibit a ...
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53 views

A problem about harmonic oscillators

A ball with mass $m$ and radius $r$ rolls without sliding inside a cylinder with radius $R (R>>r)$, with $\theta <<1$. Find the angular frequency $\omega$ What I Know: There are ...
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Reflected and refracted light have same frequency as that of the incident light frequency. Why?

My text book says- When a monochromatic light is incident on a surface separating two media, the refracted and reflected light both have the same frequency as the incident frequency. Can anyone ...
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Help understanding what the Hamiltonian signifies for the action compared with the Euler-Lagrange equations for the Lagrangian?

Consider the Lagrangian for a simple harmonic oscillator \begin{equation} L (x,\dot{x}) = \frac{1}{2}m\dot{x}^2 - \frac{1}{2}kx^2 \end{equation} Obviously we have \begin{align} \frac{\partial ...
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47 views

Uncertainty of energy for harmonic oscillator at ground state and first excited state

How does one calculate the energy uncertainty of the harmonic oscillator in the ground state and first excited state?
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How to analyse this mass-spring system

I'm trying to analyze this mass-spring system -- i.e. write down the differential equation governing it. As you can see, there is a block of mass $m_1$ attached to a wall by an ideal spring of ...
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1answer
52 views

How is a string different from a harmonic oscillator or a point?

I am reading String Theory and M-Theory: A Modern Introduction by Becker, Becker and Schwartz. I've tried to read this book before but not succeeded because I didn't know enough math or physics. This ...
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1answer
36 views

Does this massless spring affect the system?

I have to write out the differential equation modelling this system: There's a mass connected to a wall with a spring of spring constant $k_1$, sitting on a frictionless surface, with another spring ...
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60 views

Energy drain in damped oscillator

Suppose we have a mass on a spring with a damping term. The equation of motion is given by: $$m \ddot{x} = -kx - c\dot{x}$$ I believe solutions are damped oscillations of the form: $$x = x_0 ...
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51 views

The universality of the Stuart-Landau equation to describe nonlinear oscillators

I have read numerous papers which boldly suggest that the Stuart-Landau equation can be successfully used to model any weakly nonlinear oscillating system near a Hopf bifurcation. Even thought it has ...
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Can vertical SHM occur in a system of a mass between 2 springs between 2 vertical pillars? [closed]

The problem is detailed above. I have worked through problems involving SHM in the horizontal plane, but unsure how to go about it vertically. I know the weight component would need to be ...
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1answer
67 views

A pendulum in an elevator - looking upside down

If I have a pendulum connected to the floor of an elevator by a string, and the elevator is falling in an acceleration greater than g - can I just "rotate" the system and look at it as a regular ...
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88 views

Harmonic oscillator problem - Griffiths [closed]

I'm solving problems about harmonic oscillator from Griffiths book (2nd ed.) and I'm stuck in the problem 2.13. When I normalize the equation 2.51 to get $A_1$ my final wave function is complex, since ...
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1answer
33 views

Why in analysis of coupled oscillator, restoring force for uncoupled condition is taken in account?

If the pendulums were free & either one were displaced a small distance $x$, the restoring force would be $m{\omega_0}^2 x$. But in the present situation the coupling spring is stretched a ...
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72 views

How to calculate the classical on-shell action for a harmonic oscillator? [closed]

So, short and sweet, I've been reading the path integrals book by Feynman and Hibbs, and one of the elementary problems they ask is to calculate the classical on-shell$^1$ action of a harmonic ...
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1answer
125 views

Checking that the propagator for Harmonic Oscillator satisfies Schroedinger Equation [closed]

I have the propagator for the harmonic oscillator. $$K(x_f,x_0,t)=\sqrt{\frac{m\omega}{2 \pi \hbar \sin{wt}}}\exp\left(\frac{i}{\hbar}\frac{m\omega}{2 \sin{\omega t}}((x_0^2+x_f^2)\cos\omega ...
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Why does the Bohr-Sommerfeld quantization for give the exact energy-levels for a harmonic oscillator?

Why does the Bohr-Sommerfeld rule for quantization give the exact energy-levels for a simple harmonic oscillator?
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Oscillations Near Equilibrium (With Linear Differential Equations)

Case I: The force acting on an object of mass m is $F(x) = F_o(1-e^{\alpha x})$ Case II: The force acting on an object of mass m is $F(x) = F_o(1-e^{-\alpha x})$ where $F_o$ and $\alpha$ are ...
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Classical Limit of the Quantum Harmonic Oscillator

The classical harmonic oscillator obeys an arcsine law in that the distribution of positions of the particle over a single time cycle is proportional to $\frac{1}{\sqrt{A^2-x^2}}$, $A$ being the ...
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Simple harmonic motion and elasticity

Question: One end of a long metallic wire of length L is tied to the ceiling. The other end is tied to a massless spring of spring constant K. A mass m hangs freely from the free end of the ...
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112 views

An interesting problem on springs [closed]

If I place two identical objects of mass $m$ at either end of a spring with spring constant $k$ and the whole system is placed on a horizontal frictionless surface, then what is the frequency of ...