Tagged Questions
3
votes
0answers
52 views
Effective mass in Spring-with-mass/mass system
Suppose you have a particle of mass $m$ fixed to a spring of mass $m_0$ that, in turn, is fixed to some wall. I'm trying to calculate the effective mass $m'$ that appears in the law of motion of the ...
2
votes
1answer
80 views
2nd order pertubation theory for harmonic oscillator
I'm having some trouble calculating the 2nd order energy shift in a problem.
I am given the pertubation:
$\hat{H}'=\alpha \hat{p}$,
where $\alpha$ is a constant, and $\hat{p}$ is given by:
...
0
votes
2answers
53 views
Time period for spring connected body
Two identical springs with spring constant $k$ are connected to identical masses of mass $M$, as shown in the figures above. The ratio of the period for the springs connected in parallel (Figure 1) ...
1
vote
1answer
44 views
Energy eigenvalues of a Q.H.Oscillator with $[\hat{H},\hat{a}] = -\hbar \omega \hat{a}$ and $[\hat{H},\hat{a}^\dagger] = \hbar \omega \hat{a}^\dagger$
I just finished deriving the commutators:
\begin{align}
[\hat{H}, \hat{a}] &= -\hbar \omega \hat{a}\\
[\hat{H}, \hat{a}^\dagger] &= \hbar \omega \hat{a}^\dagger\\
\end{align}
On the ...
1
vote
1answer
51 views
Eigenfunctions in a harmonic oscillator
This assignment is about the one dimensional harmonic oscillator (HO).
The hamiltonian is just as you know from the HO, same goes for the energies, but I get that the wavefunction of the particle, at ...
1
vote
1answer
72 views
Pendulum in an elevator
Suppose we have a pendulum tied to the ceiling of an elevator which is at rest. The pendulum is oscillating with a time period $T$, and it has an angular amplitude, say $\beta$. Now at some time ...
4
votes
2answers
91 views
Proof for commutator relation $[\hat{H},\hat{a}] = - \hbar \omega \hat{a}$
I know how to derive below equations found on wikipedia and have done it myselt too:
\begin{align}
\hat{H} &= \hbar \omega \left(\hat{a}^\dagger\hat{a} + \frac{1}{2}\right)\\
\hat{H} &= ...
3
votes
2answers
38 views
Probability of position in linear shm?
The problem that got me thinking goes like this:-
Find $dp/dx$ where $p$ is the probability of finding a body at a random instant of time undergoing linear shm according to $x=a\sin(\omega t)$. ...
3
votes
1answer
136 views
Schrödinger equation for a harmonic oscillator
I have came across this equation for quantum harmonic oscillator
$$
W \psi = - \frac{\hbar^2}{2m}\frac{d^2\psi}{dx^2} + \frac{1}{2} m \omega^2 x^2 \psi
$$
which is often remodelled by defining a new ...
0
votes
0answers
27 views
Find Resonance Frequencies [closed]
How can I find the resonance frequencies for the harmonic dumped oscillator when it is written in this form?
$$y''\left(t\right)+2\zeta y'\left(t\right)+y\left(t\right)=\sin{(\omega t+\phi)}$$
where ...
0
votes
1answer
70 views
Standing Waves: finding the number of antinodes
A string with a fixed frequency vibrator at one end forms a standing wave with 4 antinodes when under tension T1. When the tension is slowly increased, the standing wave disappears until tension T2 is ...
0
votes
2answers
89 views
Calculating phase difference of sound waves
An observer stands 3 m from speaker A and 5 m from speaker B. Both speakers, oscillating in phase, produce waves with a frequency of 250 Hz. The speed of sound in air is 340 m/s. What is the phase ...
0
votes
0answers
36 views
How can I find the frequency? [duplicate]
Grocery stores often have spring scales in their produce department to weigh fruits and vegetables.
The pan of one particular scale has a mass of 0.5 kg, and when you place a 0.5 kg sack of potatoes ...
0
votes
0answers
50 views
Frequency with the spring scale [closed]
Grocery stores often have spring scales in their produce department to weigh fruits and vegetables.
The pan of one particular scale has a mass of $0.5 kg$, and when you place a $0.5 kg$ sack of ...
1
vote
0answers
27 views
Doubling the energy of an oscillating mass on a spring [closed]
From this question:
Question 1.
What do we need to change in order to double the total energy of a mass oscillating at the end of a spring?
(a) increase the angular frequency by $\sqrt{2}$.
...
1
vote
2answers
69 views
Potential energy during vertical fall
Suppose I have a weightless spring connected perpendicularly to the ground, and it has on top of it some weightless surface. Now, I release some sticky object from height $h$ above the system of light ...
0
votes
1answer
75 views
Simple harmonic oscillator system and changes in its total energy
Suppose I have a body of mass $M$ connected to a spring (which is connected to a vertical wall) with a stiffness coefficient of $k$ on some frictionless surface. The body oscillates from point $C$ to ...
1
vote
1answer
59 views
Why uncertainity is minimum for coherent states?
While reading for quantum damped harmonic oscillator, I came across coherent states, and I asked my prof about them and he said me it is the state at which $\Delta x\Delta y$ is minimum. I didn't ...
0
votes
0answers
58 views
Quantum harmonic oscillator. Finding operators
Problem:
I'm trying to verify that $p_H(T)$ and $x_H(T)$ satisfy the following equations, (by solving the Heisenberg equation):
$x_H(t)=x_H(0)cos(\omega t)+(1/m\omega)p_H(0)sin(\omega t)$
...
2
votes
1answer
124 views
Coordinate representation of quantum ladder operator?
I can't seem to figure out how to derive the coordinate representation of the $a_+$ ladder operator in quantum mechanics.
I know that $a_-$ is $\sqrt{\frac{1}{2mwh}} (mwx + i\dot{p}) $ in which where ...
3
votes
2answers
174 views
Constant magnetic field applied to a quantum harmonic oscillator
I have a spinless particle of mass $m$ and charge $q$ which is an isotropic harmonic oscillator of frequency $\omega_0$, then I apply a constant magnetic field in the $z$ direction. We can show the ...
1
vote
1answer
140 views
Shift operator (integral calculus involving Hermite polynomials) [closed]
I didn't know whether to pose this question on Physics.stackexchange or Math.stackexchange. But since this is the last step of a development involving the eigenfunctions of an Harmonic oscillator and ...
0
votes
0answers
98 views
Spring with mass [closed]
A block of mass $M$ is attached to a spring that has mass $m$ and the force constant $k$. The block is placed on a horizontal frictionless surface. Find the period of small-amplitude oscillations ...
0
votes
0answers
65 views
Mass spring system, increase mass [closed]
The question says that after a mass $m=M$ (attached to a horizontal spring) reaches its furthest point, so at its amplitude, the mass is doubled, $m=2M$.
What happens to the period, amplitude and ...
1
vote
3answers
477 views
Partition function for quantum harmonic oscillator
Hi guys I'm currently trying to solve a mock exam for an exam in a few days and am a bit confused by the solutions they gave us for this exercise:
Exercise:
A solid is composed of N atoms which ...
0
votes
3answers
782 views
How to derive the period of spring pendulum?
So I wanted to find out how to (simply, if that's possible) derive the formula for a period of spring pendulum: $T=2\pi \sqrt{\frac{m}{k}}$. However, Google doesn't help me here as all I see is the ...
3
votes
2answers
308 views
Dynamics of a Vertical Mass-Spring Simple Harmonic Oscillator with Gravity
I am having some trouble obtaining the elastic potential energy and gravitational potential energy of a simple mass spring system.
In this experiment, masses attached to a spring were dropped from a ...
3
votes
1answer
279 views
Writing equation for amplitude of driven harmonic oscillator in Lorentzian form
This harmonic oscillator is driven and damped, with the form:
$$\ddot{x} + \lambda \dot{x} + \omega_0^2 x = A \cos(\omega_d t)$$
Now, I have used the ansatz (guess): $x(t) = B \cos(\omega_d t + ...
0
votes
0answers
72 views
How does an oscillating particle in a non-inertial reference frame appear?
The general question is : given an oscillating particle in a non-inertial reference frame:
How would it appear from outside the non-inertial reference frame ?
How would an observer inside that ...
0
votes
2answers
285 views
Showing that the probability density of a linear harmonic oscillator is periodic
The complete question I am trying to answer is the following:
Show that the probability density of a linear harmonic oscillator in an arbitrary superposition state is periodic with period equal to ...
0
votes
2answers
148 views
Understanding the concept of period of motion in simple harmonic motion formula
I have a spring system, whose position equation is $$x(t) = c_1cos(8 \sqrt{2}t) + c_2sin(8 \sqrt{2}t)$$
The textbook says it will have a period of motion of $\frac{2 \pi}{(8 \sqrt{2}t)}$. I ...
0
votes
1answer
143 views
Spring-mass physics homework question [closed]
I've been having trouble with my physics homework. The problem is:
You may have measured the properties of a simple spring-mass system in the lab. Suppose you found ks = 0.9 N/m and m = 0.01 kg, ...
0
votes
2answers
259 views
Linear motion with variable acceleration
Consider the following problem
I pull a mass m resting at x = 0 on a frictionless table connected to a spring with some k by an amount A and let it go. What will be its speed at x=0?
I know how to ...
0
votes
0answers
493 views
Finding the period and frequency for simple harmonic motion [closed]
A 1 lb weight is suspended from a spring. Let y give the deflection (in inches) of the weight from its static deflection position, where “up” is the positive direction for y. If the static ...
0
votes
2answers
126 views
Frequency of a tuning fork in a vacuum
Consider this equation of a damped harmonic oscillator such that:
$$
\ddot{x}+2\gamma\dot{x}+\omega^2_0=0
$$
with: $\gamma=\frac{b}{2m}$ and $\omega_0=\sqrt{\frac{k}{m}}$
Finally, we know that the ...
2
votes
2answers
112 views
Force to use in harmonic oscillation through the inside of a planet
I am to find an equation for the time it takes when one falls through a planet to the other side and returns to the starting point. I have seven different sets of values - mass of object falling, mass ...
0
votes
0answers
19 views
Capsule traveling through a planet, find time for return [duplicate]
Possible Duplicate:
If it was possible to dig a hole that went from one side of the earth to the other
A corporation is building attractions in outer space, in which they drill tunnels ...
2
votes
1answer
156 views
Symbol for dashpot/damper (in a harmonic oscillator)
In diagrams that contain the dashpot symbol, sometimes the mass is attached to the "interior" end of the dashpot, other times the mass is attached to the "base" end.
For example, consider the ...
1
vote
1answer
628 views
What's wrong with this equation for harmonic oscillation?
The question:
A particle moving along the x axis in simple harmonic motion starts
from its equilibrium position, the origin, at t = 0 and moves to the
right. The amplitude of its motion is ...
0
votes
1answer
1k views
Conversion of motion equation from Cartesian to Polar coordinates: Is covariant differentiation necessary?
I have earlier posted the same question here on math stackexchange but without any answer. As the question concerns tensors, I guess that I have come to the right ...
2
votes
2answers
3k views
When are Maximum Velocity and Acceleration acheived in Simple Harmonic Motion?
Im trying to get my head around SMH out of curiosity because it seems simple yet I'm not getting the concept behind some ideas.
For a SMH equation :
$$ x=a \sin(\omega t+\phi) $$
Under what ...
0
votes
1answer
1k views
Finding Phase angle of Simple Harmonic Motion?
A sinusoidal oscillator has :
$$x=x_{max} \cos(\omega t - \varphi )$$
Period is 2, initial displacement is 100mm
initial velocity is 200mm/s
What is the phase angle assuming $-\pi < \varphi < ...
0
votes
1answer
309 views
Vibrational motion of linear diatomic molecule
This question concerns the following exercise from an old exam:
The vibrational motion of a linear diatomic molecule can be approximated as simple harmonic motion.
A CO molecule has a bond ...
0
votes
1answer
157 views
Simple Harmonic Motion. Why am I wrong? Why is my equation wrong more importantly?
Problem/Solution
!
I am deeply confused.
B) We know that
$x = 2\sin(3\pi t)$.
$x' = 6\pi\cos(3\pi t)$
So max speed is $6\pi$
$6\pi = 6\pi \cos(3\pi t)$
$\cos(3\pi t) = 1$
$3\pi t = ...
0
votes
3answers
326 views
How can I show that an arbitrary wavefunction in a 1D SHO is periodic in time?
I want to show that an arbitrary wavefunction $f$ in a one dimensional harmonic potential reproduces itself after a period T up to a phase factor: $f(x,t+T)=Af(x,t)$, $|A|=1$
I am not sure if this ...
2
votes
0answers
311 views
Amplitude of a Forced Harmonic Oscillator
For an assignment in one of my maths units at uni, I've been asked to derive and solve the differential equation of motion for a forced harmonic oscillator, with the forcing function having the form ...
3
votes
1answer
4k views
How do I solve for the phase constant given the amplitude and the angular frequency?
A piston (with mass M) in a car engine is in vertical simple harmonic
motion with amplitude A. The engine is running at a period T. Suppose
a small piece of metal with mass m were to break ...
-1
votes
1answer
1k views
What affects the damping of a spring?
What variables affect the damping of a spring executing simple harmonic motion?
What are the independent variables, and what variables would need to be controlled in an experiment?
I'm attempting to ...
4
votes
1answer
355 views
Plotting a SHO in matlab
I have no prior experience of using matlab. My teacher want me to solve this question. I have been trying for a couple of hours now with no luck, please help!
The mass of 100 g hanging in a spring ...
