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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Quantum simple harmonic oscillator interpretation

I am just wondering what does the SHO system from quantum mechanics actually physically represent? Is it just a SHO of a quantum particle, seems a little too obvious for quantum theory? I'm from a ...
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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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31 views

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

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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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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25 views

Period of small oscillations of rotational disk [closed]

This is a question on a university physics exam paper, and it doesn't seem immediately intuitive how the problem works. The answer is given, but not any details of the working. Also, I'm not sure if ...
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37 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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91 views

Spring Stiffness Calculation Problems

This may sound like a trivial question but please hear me out. I am trying to model a 1 DoF electromagnetic vibration sensor (geophone) analytically and with finite elements. A geophone consists of ...
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1answer
42 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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54 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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38 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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923 views

Coupled quantum harmonic oscillator

Given the following Hamiltonian for two identical linear oscillators with spring constant $k$ and interaction potential $\alpha x_1x_2$; I was asked to find the expectation value $\langle ...
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29 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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194 views

Questions related to resonance/standing-waves and sound

I understand resonance for a simple harmonic oscillator but not for more complex systems like standing waves. How can I be in resonance with the normal mode in an organ pipe? I understand that the ...
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36 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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42 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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81 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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219 views

Why is $\pi$ used when calculating the value of $g$ in pendulum motion?

I am trying to intuitively understand why $\pi$ is used when calculating the value of $g$ using the harmonic motion of a pendulum: $$g ~=~\frac{4\pi^2L}{T^2}.$$ Does it have something to do with the ...
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39 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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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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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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47 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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243 views

Does damping force affect period of oscillation?

In my physics notes, it has been given that the damping force increases the period of oscillation. I am unable to understand this part. How is this possible? The only relation I know is that as the ...
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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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limit as $x_1 \to x_0$, propagator for the harmonic oscillator

Consider a non-relativistic particle of mass $m$, moving along the $x$-axis in a potential $V(x) = m\omega^2x^2/2$. use path-integral methods to find the probability to find the particle between ...
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60 views

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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Why is the harmonic oscillator so important?

I've been wondering what makes the harmonic oscillator such an important model. What I came up with: It is a (relatively) simple system, making it a perfect example for physics students to learn ...
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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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51 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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2k views

Average Energy of the Quantum Harmonic Oscillator

In Griffiths, the average potential energy for the quantum harmonic oscillator is given as $$\langle V\rangle~=~\frac{1}{2}\hbar \omega(n+\frac{1}{2}).$$ Is the potential energy of the quantum ...
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59 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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960 views

Can a simple pendulum be considered a simple harmonic oscillator?

Is the motion of a simple pendulum, a simple harmonic motion? It stops vibrating after sometime.
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Energy of damped harmonic oscillator begins to increase with very large Q in numerical integration

I have numerically integrated the (reduced) homogeneous equation of a damped harmonic oscillator in order to see how the error propagates. $$\frac{d^2 X}{d\phi^2} + ...
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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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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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79 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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30 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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108 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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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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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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Pressure in Harmonic Oscillation

Classical Harmonic oscillator's energy depends on temperature as it equals $k_B$$T/2$. However, quantum harmonic oscillator energy is $(n+1/2)hf$. So, when T=0, quantum predicts motion. I have been ...
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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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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 ...
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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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Very confused about effective spring constant

I know that for springs in parallel, the effective spring constant is $k_1+k_2$ and for springs in series the constant is $1/(1/k_1+1/k_2)$. But there are some weird problems where finding the ...
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104 views

Transition Probabilities for the Perturbed Harmonic Oscillator

I consider the following Hamiltonian $$H=\frac{p^2}{2m}+\frac{m\omega^2}{2}x^2+\Theta(t)Fx,$$ where $F$ is an external constant force. So the Hamiltonian describes an unperturbed harmonic oscillator ...