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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Meaning of “Simple” in Simple Pendulum and Simple Harmonic Motion?

I have gone through the Phys.SE question Why is simple harmonic motion called so?. From the 1st answer of this Question it seems to me that another type of "Harmonic motion" is "Damped Harmonic Motion"...
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Particle attached in equilibrium to two elastic strings

The question I'm trying to answer is this: This is the solution: The only part of the solution I have a problem with is $x_{ps} + x_{qs}=l$, where $x_{ps}$ is the extension of the string from $P$ ...
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117 views

Finding the Expectation value of harmonic oscillator [on hold]

What is the expectation value for $e^{{\alpha}a^{\dagger}}e^{-\alpha^*{a}}$ of any two states of harmonic oscillator (let say $|n\rangle$ and $|m\rangle$) given below, $$\langle n|e^{{\alpha}a^{\...
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2answers
69 views

Completeness relation for coherent states of the quantum harmonic oscillator

For the Quantum harmonic oscillator with energy eigenstates $|n\rangle$ one defines a coherent state for every complex number $z$ by setting (note that the normalization varies across the literature) $...
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Simple harmonic motion [closed]

A body executing shm has 10cm as amplitude and time period is 1.5s. Calculate the time taken by the body to travel a distance 5√3 cm from the mean position. I have used the formula x=asim(wt) And ...
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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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23 views

Probability of expectation value of energy wave function at initial time [closed]

If a quantum harmonic oscillator wave function with energies $$E_n = (n+1/2)\hbar\omega$$ is given by $$\Psi(x,0)=\frac{1}{\sqrt{10}}\left[3\phi_0(x)+\phi_1(x)\right]$$ where $\phi_0(x)=\left(\frac{m\...
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1answer
31 views

Existence of stationary solutions to the Liouville equation for the harmonic oscillator

So I was trying to solve the Liouville equation, which for the classical harmonic oscillator in one dimension looks like this: $$\frac{\partial \rho }{\partial t} + \frac{p}{m} \frac{\partial \rho }{\...
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1answer
52 views

How would you go about solving this difficult physics problem? [closed]

I was able to calculate an angular frequency of 85.4357 rad/s for this mass. However, I am confused as to what to do next. Any ideas?
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1answer
190 views

Cause of SHM of liquid-column in V-tube

Suppose there is a v-shaped tube filled with water. The left limb is at $\theta_1$ & the right limb is at $\theta_2$ with the horizontal base. Initially, the level of water in both the columns are ...
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111 views

Is it a coincidence that quantum harmonic oscillators and photons have energy quantised as $E=hf$?

I have studied the quantum harmonic oscillator and solved the Schrodinger equation to find the eigen-energies given by $$ E_n = \left(n+\frac{1}{2}\right)\hbar \omega. $$ Which means the energy ...
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2answers
21 views

Vertical and Horizontal Oscillations With the same period and speeds

Why do vertical and horizontal springs with the same masses attached oscillate with the same period and the same speeds at matching positions? Assume that the horizontal surface is frictionless and ...
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1answer
134 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 equation of ...
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1answer
75 views

Harmonic oscillator in quantum mechanics

I have brief questions regarding the attachments, which are notes from the book Introduction to Quantum Mechanics by Griffiths which explains the harmonic oscillator case. Any assistance would be ...
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2answers
48 views

Simple harmonic motion mass between 2 buildings

I have a question, where I have a mass on top of a building, we give it initial velocity of $\sqrt{gd/2}$ then it starts colliding between 2 buildings, elastic collision. I have to find how many times ...
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1answer
131 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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1answer
241 views

Understanding transverse oscillation in 1 mass, 2 spring systems

Lately I have been working through some nice problems on mass-spring systems. There are tons of different configurations - multiple masses, multiple springs, parallel/series, etc. A few possible ...
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3answers
66 views

Oscillations in U-tube [duplicate]

U-tube, of uniform cross section $S$ and opened at both ends, is filled with a liquid column of length $L$ and density $\rho$. In equilibrium the water levels in both arms are at same height. What ...
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2answers
2k 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 x_1x_2\...
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1answer
136 views

What is the effect of liquid density on the pitch of a singing wine glass?

In the singing wine glass experiment what's the effect on the frequency produced if the effect of liquids with different densities was tested? Everything else would be kept constant (same glass, ...
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2answers
146 views

Does spatial coupling prohibit resonances due to an external source field?

The harmonic oscillator coupled to a sinodial external source $$\frac{\partial^2 x(t)}{\partial t^2}+\omega_0^2 x(t)=F_0\sin(\omega_\text{ext}\ t),$$ has the solution $$x(t)=x(0)\cos(\omega_0 t)+C \...
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27 views

Seesaw pendulum period

If I have a rigid pendulum of length $L$, with the pivot point set somewhere along $L$ and a mass at each end how do I calculate its maximum speed and its period? I want to make a counterbalanced slow ...
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1answer
447 views

How to derive the time period equation for a spring mass system taking into account the mass of the spring without involving energy analysis?

I want to know the way to derive the time period equation of a spring mass system accounting for the mass of the spring but not using the energy analysis method but by proceeding in the same way as we ...
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2answers
47 views

Harmonic motion equation - non-null right hand side

Considering the following motion equation : \begin{equation} \ddot x + \frac{a^2 b^2}{c^2} x = -V \frac{a b}{c^2} \end{equation} where $a$, $b$, $c$ and $V$ are all constant. One can identify the ...
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2answers
33 views

Springs acting on a car [closed]

I am trying to solve a problem but I can't figure out why the answer comes out to be what it is: A man of 80kg enters a car and compresses the 4 springs of the car, causing a change of 1,2cm from ...
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2answers
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Why is the damping force acting on an oscillating system opposite in direction to velocity and not acceleration?

So far I know that the damping force is a frictional force that opposes motion and so it acts in the opposite direction to velocity . Bit why can't the same be said for acceleration doesn't the ...
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Mechanical energy in an harmonic wave and in normal modes

I think I miss something about energy of a mechanical wave. In absence of dissipation the mechanical energy transported by an harmonic wave is constant. $$E=\frac{1}{2} A^2 \omega^2 m$$ But, while ...
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35 views

Oscillation of a simple pendulum [closed]

What is maximum possible time period of oscillation of a simple pendulum on earth? Please elaborate your answers.
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90 views

How to form the matrix representation of $|O|^3$

I'm interested in getting the matrix representation of the absolute value of an operator. I know the matrix representation of the operator $O$. Now how do I take its absolute value?
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95 views

The “harmonic paradigm” in physics

Disclaimer: I know this is a vague question, so if this is not the appropriate thread, please direct me to the correct one. On page 5 of Anthony Zee's Quantum Field Theory in a Nutshell he speaks of ...
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1answer
44 views

Expectation energy for a quantum harmonic oscillator

At 59:14 in this video, the expectation value of the energy of a harmonic oscillator is $$ \langle E \rangle = \int ||\tilde{\Psi}(p)||^2 \frac{p^2}{2m}\ \mathrm dp + \int ||\Psi(x)||^2\frac{m\omega^2}...
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Modelling a flow due to an oscillating hemisphere?

Say I have a long cylinder filled with air, closed at one end and open at the other. Now say I place a compressible hemisphere at the closed end and make it oscillate (compression and expansion of the ...
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29 views

Galileo's pendulum and any references

In some texts about the simple pendulum we use to see references about some "experiments" Galileo Galilei did realize and whereby he found some important results, including that the period of the ...
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1answer
68 views

Understanding Quantum Harmonic Oscillator derivation

I'm using this pdf as a reference. Basically, I want to solve equation 0.3, which can be simplified to equation 0.5. The solution is in the form $$ \Psi(u)=h(u)e^{\frac{-u^2}{2}}$$ where $h(u)$ can ...
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0answers
37 views

How can $\hat p = - i \hbar \partial_q$ be derived starting from the definitions of $\hat q$ and $\hat p$ in terms of creation/destruction operators? [duplicate]

Consider the position and momentum operators $\hat q$ and $\hat p$, defined respectively in terms of creation and destruction operators in the usual way: $$ \hat q = c (\hat a + \hat a^\dagger), \...
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Relation between Qualiy factor and FWHM

I know how to show that the Quality factor $Q=\omega/\nu$ of a damped harmonic oscillator (for example like in this link: http://farside.ph.utexas.edu/teaching/315/Waves/node11.html). What I don't ...
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4answers
53 views

Pendulum and simple harmonic motion

I have a physical pendulum that, for small oscillations, can be modeled with the simple harmonic motion approach. In determining the motion equation, I need to figure out the amplitude: I know that ...
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1answer
72 views

Common basis for angular momentum and Hamiltonian, harmonic oscillator

Suppose a two dimensional isotropic harmonic oscillator. We define the angular momentum operator as $L = XP_y - YP_x$, where $X,Y$ are the position operators and $P_x,P_y$ are the momentum operators. ...
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Relationship between zero modes and symmetry in a simple system of coupled springs

This Wikipedia page states that "zero modes appear whenever a physical system possesses a certain symmetry," and gives the example of a ring of beads connected by springs having a zero mode associated ...
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1answer
4k 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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2answers
42 views

Independence of Period and Amplitude in Simple Harmonic Motion

In Simple Harmonic Motion, the period $T$ of an oscillation, is said to be independent of the amplitude $A$ of an oscillation, but why is that so? Attempting to derive from the equations of Simple ...
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2answers
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Eigenstates of a shifted harmonic oscillator

Let's say I have a quantum harmonic oscillator $H = \omega a^\dagger a$, where $a^\dagger$ is the raising operator and $a$ is the lowering operator and $H |n\rangle = \omega n |n\rangle$. Now assume ...
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Why is the simple harmonic motion idealization inaccurate?

While in my physics classes, I've always heard that the simple harmonic motion formulas are inaccurate e.g. In a pendulum, we should use them only when the angles are small; in springs, only when the ...
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1answer
41 views

Is this a valid way for deriving the ODE for a lattice vibration of a one dimensional crystal?

Consider the following lattice: I want to derive a differential equation that describes the forces acting on the $n$-th atom in the lattice. Each atom is coupled to its neighbour ($n+1,n-1)$ by a ...
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1answer
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normal force on a physical pendulum [duplicate]

I have read and understood that a normal force has got nothing to do with torque on a physical pendulum. But I can't understand in which direction the normal force points to. Can someone help? This ...
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Pendulum in Accelerating Elevator

I have been looking for this for quite some time now. A simple pendulum behaves in SHM. Let's put that pendulum in an upward accelerating elevator. The component of the force that acts in SHM $(\text{...
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1answer
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When a particle oscillates with simple harmonic motion, the period of the oscillation is [closed]

When a particle oscillates with simple harmonic motion, the period of the oscillation is... a) ...directly proportional to the displacement from the origin b) ...directly proportional to the ...
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1answer
46 views

Why does a bungee jumper continue to move downwards beyond the equilibrium position of the jumper and cord?

When a bungee jumper jumps, ignoring the mass of the bungee cord, the jumper initially falls in freefall before an inelastic collision occurs between the jumper and cord, and the cord extends as the ...
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77 views

Resonant Frequency of 2 mass spring system

So the question goes if I has a spring with spring constant $k$ and two masses attached to this spring (one on either side) what is the resonant frequency of the system in terms of $m$ and $k$? ...
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Why do standing waves only occur in some specific conditions?

In the string which has both end fixed then the end point have to be $n (\lambda/2)$ from the beginning point in order to have standing waves. I know it has to start with a node and end with a node, ...