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.

learn more… | top users | synonyms (1)

0
votes
0answers
17 views

Where can I add a mass to influence the period of a light pendulum the most

Using a small angle approximation $$T=2 \pi \frac{I^{1/2}}{g\tau^{1/2}} $$ so for a light pendulum $$T=2\pi\frac{l^{1/2}}{g^{1/2}}$$ So with a light pendulum of mass M with a small mass at x this ...
0
votes
1answer
17 views

Period of a spring in SHM (simple harmonic motion)

An object with unknown mass M is hanged on a vertical spring with unknown spring constant K, the spring is in rest and is 14 cm from its normal point (if it didn't had the mass hanged it had less 14 ...
0
votes
1answer
34 views

Density of states of 3D harmonic oscillator

for the first red box, shouldn't be $\epsilon^2 =\epsilon_{n_x}^2 +\epsilon_{n_y}^2 + \epsilon_{n_z}^2 + 2\epsilon_{n_x}\epsilon_{n_y} + 2 \epsilon_{n_x}\epsilon_{n_z} + ...
3
votes
3answers
95 views

Is it possible to write the fermionic quantum harmonic oscillator using $P$ and $X$?

The Hamiltonian of the quantum harmonic oscillator is $$\mathcal{H}=\frac{P^2}{2m}+\frac{1}{2}m\omega^2X^2$$ and we can define creation and annihilation operators ...
-1
votes
0answers
25 views

Does Kinetic energy of a simple harmonic motion system change if mass is removed?

Let's say you have a mass oscillating with 50 joules of potential energy in the system. If you remove half of the mass (without applying any forces), will the simple harmonic motion system retain all ...
0
votes
0answers
63 views

Simple Harmonic Motion Mass and Amplitude [closed]

You (mass m1 = 77.5 kg) stand on a platform of mass m2 = 21 kg. The platform executes simple harmonic motion with a period of 2.55s. WHen the platform is at maximum displacement, you step off the ...
0
votes
1answer
44 views

Finding the spring constant in SHM question [closed]

This question has got me confused, due to the fact that it says that the particle starts off at a negative amplitude, passes equilibrium, then has a positive velocity while moving back towards ...
-4
votes
0answers
23 views

How can I find the equation of motion? [duplicate]

There is a point of mass moving in the xy-plane with harmonic forces acting in x- and y-direction $F_x=-m\omega^2x$ and $F_y=-m\omega^2y$. At the same time there is an additional force acting in the ...
0
votes
1answer
61 views

Pendulum on the moon, (Highschool)

A simple pendulum used as a clock, set with the correct time at earth, was sent to moon, it was noticed that it is late 36mins for each hour on earth. Calculate the ratio between acceleration of ...
1
vote
1answer
49 views

Lax representation of the harmonic oscillator

Peter Lax showed that the differential operators $$L=-6\partial_x^2-u,\quad B=-4\partial_x^3-u\partial_x-(1/2)u_x$$ fulfilling the Lax equation $$\dot{L}+[L,B]=0$$ is equivalent to the KdV equation ...
1
vote
0answers
17 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 ...
0
votes
1answer
36 views

Trick for reformulating in terms of centre of mass and relative variables

I am working through a problem that has caused me difficulties in the past. I have the Hamiltonian $$\mathcal{H}=\frac{p_1^2}{2m_1}+\frac{p_2^2}{2m_2}+\frac{k}{2}(q_1-q_2)^2$$ I want to express the ...
0
votes
0answers
40 views

Finding the phase space density of $N$ harmonic oscillators

Consider a system of $N$ identical harmonic oscillators in 1d. The Hamiltonian will be given by $$\mathcal{H}_N=\sum_{i=1}^N \frac{p_i^2}{2m}+\frac{m\omega^2}{2}q_i^2$$ Now supposedly the Hamiltonian ...
1
vote
0answers
10 views

Where is there posted dampening coefficients for viscous dampers?

Depending on the size of the viscous dampener the coefficient will change, however i am trying to model a "physical" system with calculating everything out, so that way i can test failure before it ...
1
vote
1answer
41 views

What are the units of the creation and annihilation operators?

The creation and annihilation operators - also known as ladder operators are; $ \hat{a}^\dagger$ and $\hat{a}$ respectively. Using the equation $\hat{H} = \hbarω\left(\hat{a}^\dagger \hat{a} + ...
1
vote
1answer
32 views

Pendulum at an angle

A pendulum has a period of $T$ when swinging from a string. The pendulum is now placed on a frictionless incline at a 30 degree angle. What is the new period of the pendulum?
1
vote
1answer
29 views

How to find the spring coefficient of a simply supported beam?

So I've been searching wikipedia and google but nothing can show how to find the spring coefficient of a simply supported beam with a uniformly distributed load. The spring coefficient, $k$, is ...
0
votes
0answers
12 views

Usage of concept of static deflection on classical mechanics (ex. SHM based problems)

Can anyone explain how the concept of static deflection (static displacement) is used in problems of SHM? Explanation by/with an illustration would be even the more helpful. Thank you
1
vote
2answers
41 views

Using fluid mechanics to show that force is directly proportional to velocity

So I am writing a paper about viscous dampers in harmonic oscilators, however I was looking at some old fluid mechanic notes and I thought I had come across what I needed although I have gotten stuck. ...
4
votes
2answers
86 views

“Equidistant” spectra in quantum mechanics [duplicate]

In one-dimensional quantum mechanics, it seems that the only kind of potential able to produce an "equidistant" spectrum, i.e. with $E_{n+1}-E_{n}=\text{constant}$, is the harmonic oscillator. Why is ...
1
vote
2answers
35 views

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 ...
-2
votes
1answer
37 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 ...
5
votes
1answer
79 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 = ...
0
votes
1answer
47 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 ...
5
votes
2answers
507 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} = ...
0
votes
1answer
36 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 ...
0
votes
0answers
49 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 ...
0
votes
1answer
20 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 ...
1
vote
1answer
40 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 ...
2
votes
1answer
74 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 ...
0
votes
0answers
37 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 ...
-1
votes
2answers
53 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 ...
0
votes
1answer
31 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 ...
0
votes
2answers
42 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 ...
0
votes
1answer
28 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}} = ...
0
votes
1answer
106 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 ...
0
votes
1answer
63 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 ...
1
vote
1answer
51 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 ...
1
vote
2answers
65 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 ...
0
votes
1answer
95 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 ...
1
vote
1answer
43 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 ...
0
votes
2answers
183 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 ...
0
votes
2answers
39 views

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? ...
0
votes
2answers
97 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. ...
1
vote
1answer
56 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 ...
3
votes
1answer
56 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 ...
2
votes
1answer
26 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 ...
0
votes
1answer
57 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 ...
4
votes
2answers
381 views

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 ...
1
vote
4answers
198 views

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 ...