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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Fluid filled harmonic oscillator

A vessel (preferably circular) filled with water is accelerating unidirectionally such that the level of water is higher on one end than the other. What I want to know is that if the vessel is ...
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221 views

Combination of Simple Harmonic Motions

Will the combination of 2 Simple Harmonic motions will be an SHM in itself? For example for simple functions such as $$\ f(t)=\sin\omega t-\cos\omega t$$ I can use trigonometry to show that it can ...
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29 views

AFM cantilevers driven below resonance?

Is there a physical reason why AFM cantilevers are driven below their resonance frequencies? In all of the AFMs I have used, once you measure the resonance frequency of the cantilever, it is set up ...
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33 views

Block-Spring System Kicked Into Motion

Given two blocks of identical mass on a frictionless surface and connected by a spring with spring constant k, I'm asked to find the motion of the blocks -- after one is kicked into motion with ...
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1answer
63 views

Is there an easy way to treat the anisotropic harmonic oscilator?

In Quantum Mechanics we can deal with the one-dimensional harmonic oscilator by using the trick of the ladder operators. In that case, the original Hamiltonian is $$H = ...
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67 views

Do you know the principle which says that connecting two sources of similar kind produces a waste and destruction? [closed]

There is a great article, called commutation cells, which states that you cannot transfer kinetic energy from one container to another immediately, bypassing the potential energy storage. Otherwise, ...
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1answer
81 views

Why $k/m$ in simple Harmonic motion equal $\omega^2$? [closed]

I've come across this thing in simple harmonic motion but never did I manage to find a reason why $k/m$ should equal $\omega^2$ and the theory behind it. People say it is done for convenience equating ...
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1answer
87 views

Why are harmonic oscillators quantized? [closed]

What physical reason is there for a mass on a spring to have discrete energy levels? And why are those energy levels equally spaced, i.e. why is $E \ \alpha \ f$? Personal background and ...
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27 views

I do not understand why $a_-a_+\psi_n=(n+1)\psi_n$ and not $\sqrt n(n+1))\psi_n$ [duplicate]

I do not understand why $a_-a_+\psi_n=(n+1)\psi_n$ and not $\sqrt n(n+1))\psi_n$ or how the Energy formula can help me understand this (I was told that it would). In the introduction to quantum ...
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1answer
63 views

I do not understand why $a_-a_+\psi_n=(n+1)\psi_n$

I do not understand why $a_-a_+\psi_n=(n+1)\psi_n$ and not $\sqrt n(n+1))\psi_n$ or how the Energy formula can help me understand this (I was told that it would). In the introduction to quantum ...
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65 views

Quantum harmonic oscillator, clarification about the period

We can write the general state |A> at time $t=0$ as $|A, 0>=\sum a_n |n>$ where |n> are the eigenvectors of the oscillator. In my textbook there is written that if the $a_n=0$ for every n=even ...
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32 views

Resonance of a system featuring a collection of individual resonators?

Suppose you had a number of harmonic oscillators, each with different resonant frequencies in a system. Does this imply that their is an overall system resonance that is dependent on the individual ...
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44 views

Harmonic oscillator homework question [closed]

A penny rests on a piston as it undergoes vertical harmonic motion, which has an amplitude of 0.04m, what is the maximum frequency of the oscillator such that the penny does not lose contact with ...
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1answer
43 views
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1answer
71 views

Total energy of a simple pendulum proportional to the square of the amplitude? [duplicate]

It is known that in simple harmonic motion, the total energy of the system is proportional the square of the amplitude, but how can I prove that for a simple pendulum where amplitude is the arc length ...
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1answer
51 views

Mismatch between underdamped and critically damped solutions

If you have a harmonic oscillator with damping $D$ (e.g. small angle pendulum) $$\ddot{\theta}+D\dot{\theta} + \theta=0$$ then the solution I get in the underdamped case ($D^2-4<0$) is: ...
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60 views

Perturbation theory of $\lambda q^4$ perturbed harmonic oscillator

For a perturbed Hamiltonian $$ H = H^{(0)} + H' $$ the perturbation theory approach $$ \Psi = \Psi^{(0)} + \lambda \Psi^{(1)} + ... \\ E = E^{(0)} + \lambda E^{(1)} + ... $$ leads to the equations ...
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3answers
158 views

Simple harmonic motion versus oscillations

I want to see whether certain oscillations in my daily life, such as the oscillation of violin strings when plucked, are simple harmonic motion or not. Can we identify whether an oscillation is simple ...
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2answers
67 views

Physical interpretation of Fourier $[x(t)]$ where $x(t)$ is the position of mass $m$ as a function of time?

If a macroscopic body of mass $m$ moves according to a certain law of motion like, for example, $$x(t)=A\cos(2\pi ft)$$ then what physical interpretation can be attributed to the Fourier transform of ...
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49 views

Coupling of LC circuits

I am reading an old article in a physics journal in which the author explains that the frequency between two identical, but capacitively coupled oscillators becomes ...
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1answer
45 views

Why does the potential in simple harmonic motion contain only even powers?

The lecturer was showing that any system (almost) will behave as SHM if we move it by a small $\alpha$ from its equilibrium point. For doing so, he wrote the potential of the motion as ...
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1answer
94 views

Spring-mass system with complex spring constant

Suppose a system containing a mass $m$ on frictionless surface, attached by a spring to a wall. The spring's constant is complex, given by $K = K_1 + K_2i$, with $K_1 \gg K_2$. Write the ...
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2answers
147 views

Exact closed form solution to the quantum harmonic oscillator

I came across this question in Griffiths QM, which asked to show that this equation $$\Psi(x,t)=\left(\frac{m\omega}{\pi \hbar}\right)^{1/4} \exp\left[-\frac{m\omega}{2\hbar} ...
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1answer
87 views

Why does $\omega = \sqrt{V''(x_0) / m}$?

I know that in an equation such that $$\ddot{x} + \omega^2x = 0,$$ the angular frequency $ = \omega$. But why is that ever $ \sqrt{V''(x_0) / m}$? (where $x_0$ is the equilibrium point). I just saw ...
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1answer
108 views

An overdamped oscillator with natural frequency ω and damping coefficient γ starts out at position x0 > 0 [closed]

An overdamped oscillator with natural frequency ω and damping coefficient γ starts out at position x0 > 0. What is the maximum initial speed (directed toward the origin) it can have and not cross the ...
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1answer
52 views

Initial conditions for shm [closed]

This is the part of the question from the book that I am studying, "A mass of $0.75\:\mathrm{kg}$ is attached to one end of a horizontal spring of spring constant of $400\:\mathrm{N m^{−1}}$. The ...
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1answer
123 views

How to find frequency with only amplitude? [closed]

I came across the following problem earlier. A platform oscillates in the vertical direction with simple harmonic motion. It’s amplitude of oscillation is C. What is the range of frequency of ...
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1answer
58 views

Oscillating Ruler

I was bored in the office and stuck a ruler in my desk and started maing it oscillate. I noticed that when I looked at it from the top, there were some bands of color I observed (as in the pic below) ...
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2answers
59 views

Energy of driven dampened oscillator

Given the oscillator described by: $$m\ddot{x}+\gamma \dot{x}+kx=F_0\cos(\omega t)$$ And supposing the system is at it's stable state, I wish to calculate the following: 1) The system's energy at any ...
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1answer
41 views

Simple harmonic motion, maximum kinetic energy [closed]

Why kinetic energy is maximum at mean position?
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21 views

How to apply cutoff in path integral?

I am working on harmonic oscillator for quantum fluctuations (apart from clasical part), path may written as $$ S_q=\int_0^Tdt[(\partial_tq)^2+w^2q^2] $$ This may written as $$ S_q=\int dt(q\Delta q) ...
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1answer
55 views

Excitation source in 2D grid coupled harmonic oscillator

In A. Zee's Quantum field theory in a Nutshell, he describes the QFT analogy of a matress, a 2D grid of points $q_a$ connected by springs (first page of first chapter, $q_a$ is the vertical ...
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1answer
100 views

Motion of Thompson's jumping ring

Thompson's jumping ring experiment is set up as follows: There is a force acting on the ring $F(x)$ where $x$ is the vertical displacement. The force is due to the $90^\circ$ out of phase flux ...
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452 views

Pendulum's motion is simple harmonic motion

For a pendulum's motion to be simple harmonic motion (S.H.M.) is it necessary for a pendulum to have small amplitude or S.H.M. can be produced at large amplitudes as well? If it is really necessary ...
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2answers
39 views

Proportionality of states in quantum harmonic oscillator

What is the justification for $a_{\pm} \psi_{n}$ being proportional to $\psi_{n\pm1}$ in a quantum harmonic oscillator? Here $a_{\pm}$ is the raising/lowering ladder operator.
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44 views

Solution to Harmonic Oscillator

The damped oscillator is governed by the equation of motion: $\ddot{x} + 2\beta \dot{x}+\omega _{0}^2x=0$ where $\omega _{0}=\beta$ for an oscillator with critical damping. The solution is $x(t)= ...
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1answer
48 views

Driven harmonic oscillator problem : change of variables and expressing the extension of the spring

I'm struggling to understand the reasoning in question $b)$. Basically, I had to write Newton's Second Law and do a change of variables to put the equation of motion of a mass $m$ in a specific form, ...
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1answer
249 views

Spring-block system, simple harmonic motion, time period

In the case of simple harmonic motion of spring block system, why time period of the simple harmonic motion of the block is independent of acceleration of the system (spring-block system)?
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132 views

Calculating trajectory of particle moving in a potential (SHM)

I have been given the potential of a simple harmonic oscillator: $$V=\frac{1}{2}kx^{2}$$ I want to calculate the value $x(t)$ of a particle moving in this potential, with initial conditions ...
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1answer
66 views

Response functions for the quantum harmonic oscillator

I'm going through problems in Quantum Field Theory for the Gifted Amateur, and have been trying to understand a problem on the forced quantum oscillator [$L = ...
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1answer
56 views

Derive an equation related to magnetism [closed]

Solve the equations for $v_x$ and $v_y$ : $$m\frac{d({v_x)}}{dt} = qv_yB \qquad m\frac{d{(v_y)}}{dt} = -qv_xB$$ by differentiating them with respect to time to obtain two equations of the ...
2
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0answers
51 views

Simulation of oscillator with frequency dependent damping

What would be the equation for the frequency dependent damping of harmonic oscillator? Is there something like: $$ \ddot{x}+2\delta\dot{x}+\omega_0^2x = \frac{F}{m}f(t) $$ with frequency dependent ...
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1answer
112 views

Probability current for electron in uniform magnetic field: wave function forever splitting apart?

In this document http://hitoshi.berkeley.edu/221a/landau.pdf on Landau levels, in section 4, page 19, "Transitionally invariant Gauge", they analyze the free electron in a uniform magnetic field ...
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1answer
189 views

Area of phase space of Harmonic oscillator

We all know that the phase trajectory of an undamped linear harmonic oscillator is an ellipse. But when we calculate the area of the ellipse we find it does not depend of mass of the particle. Why is ...
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2answers
53 views

Quantum harmonic oscillator - Where am I going wrong?

Find the relationship between $a_+\psi_n$ and $\psi_{n+1}$ My attempt: I was able to prove that $\int{(a_+\psi)^*(a_+\psi)dx} = \int{\psi^*({a_-a_+\psi})dx}\qquad\qquad (1)$ And, ...
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1answer
86 views

Number of states in a given Landau level

For an electron in a uniform magnetic field, in free space, we seek to find the number of allowed states in a given rectangle $L_x L_y$ (for some fixed Landau level). In effect we are tiling 2-D ...
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1answer
207 views

$N$ coupled quantum harmonic oscillators

I want to find the wave functions of $N$ coupled quantum harmonic oscillators having the following hamiltonian: \begin{eqnarray} H &=& \sum_{i=1}^N \left(\frac{p^2_i}{2m_i} + ...
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1answer
110 views

Density of states of classical harmonic oscillator in phase space

Since all classical harmonic oscillators are ellipses in phase (position-momentum) space, and since the entire phase trajectory of a given system (with a fixed rigidity and mass factor) can be ...
3
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1answer
90 views

State time evolution of a quantum harmonic oscillator with a Dirac-Delta function as an initial state [closed]

I have a question just like this Phys.SE problem here with a difference that our system is a harmonic oscillator (rather than a free particle). A particle with mass $m$ is connected to a string with ...
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133 views

Why would the relationship between period and mass be important to you in a Simple Harmonic motion?

My lab's teacher always asks us why we're there at lab before the class starts. We already know the variables we're supposed to measure, so we frequently say (We used to say): "We want to find out the ...