Questions tagged [harmonic-oscillator]

The term "harmonic oscillator" is used to describe any system with a "linear" restoring force that tends to return the system to an 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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32 views

Resonant response of oscillator [closed]

Within my lectures on SHM we covered the basics of resonance. To get an equation for displacement one step was used which I am not comfortable with. My lecturer said that there is a perfect balance ...
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85 views

Demonstration of Simple harmonic motion and Hooke's law

Im very new physic student. Im studying this video. https://www.youtube.com/watch?v=tNpuTx7UQbw&index=11&list=PLyQSN7X0ro203puVhQsmCj9qhlFQ-As8e it's about Simple harmonic motion and hooke's ...
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68 views

Would this be considered simple harmonic motion?

If a small creature moves in a vertical circle, will its shadow formed on a horizontal plane, because of the sun, move in a simple harmonic motion? I'm considering it to be a small circle so that the ...
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2answers
749 views

Harmonic oscillator at finite temperature: taking expectation values of operators

I have the Hamiltonian of an harmonic oscillator (with $\hbar=1$) $$ H = \omega \left(a^\dagger a + \dfrac{1}{2} \right) \;, $$ and the associated (canonical) partition function $$ Z = \text{Tr}\left[...
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43 views

How do we verify the value of $x$ particular that's been given as $f/k$ in this lecture? [closed]

I was watching this lecture about Simple Harmonic Motion and how the friction plays a role in the SHM of a block connected to a spring that's connected to a wall. I don't understand how the value of $...
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1answer
512 views

Deriving an expression for the spacing of bumps on the road given that the car suspension is resonating [closed]

The suspension of a car may be considered to be an ideal spring under compression. When the driver, of mass $m_1$, steps into the car, of mass $m_2$, the vertical height of the car above the road ...
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282 views

Damped Harmonic Oscillator Scenario

Suppose we have the following setup, a mass on a spring attached to a wall, as shown in the diagram: We are completely ignoring friction between the mass and the ground here, and we have an ideal ...
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76 views

In this experiment to determine the maximum frequency of oscillation, why is it important that the position of the mass stays constant?

A metal plate is attached to vibrator. A small mass of 'm' kg is placed on the metal plate. The frequency of the vibrator is increased until the mass leaves contact. This frequency is thought to ...
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26 views

A context-based simple harmonic question

The question I'm trying to understand is part b) of this: For part a) I calculated the angular velocity to be $\pi$ rad$s^{-1}$ by solving $T=\frac{2\pi}{ω}$, where $T=2$s. Then I used $v_{max}=aω$ ...
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1answer
584 views

Which mode is a cantilever oscillating at when twanged at one side and changing the length? [duplicate]

so I am measuring the relationship between the period and length of a cantilever beam, and I came across a huge roadblock. Apparently the relationship is but I don't understand what the mode has to ...
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65 views

Time evolution $x(t)$, $p(t)$

For the one-dimensional harmonic oscillator, if $U(t,0)$ is the time-evolution operator, why $$ x(t_{0})=U(t_{0},0)\cdot x(t)\cdot U(-t_{0},0) $$ $$ p(t_{0})=U(-t_{0},0)\cdot p(t)\cdot U(t_{0},0) $$ ...
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170 views

How do I evaluate the expectation value $\left \langle \hat{p}^{2} \right \rangle$ for a quantum harmonic oscillator? [closed]

The probability function of a quantum SHO is: $$P(x)=Ae^{-\frac{x^{2}}{\sigma ^{2}}}$$ where $A$ is a factor required for normalisation. The operator is: $$\hat{p}^{2}=(-i\hbar\frac{\textrm{d}}{\...
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2answers
98 views

A conceptual doubt regarding Longitudinal Waves

I was recently studying about Longitudinal Waves and I have a little trouble understanding the Displacement versus distance graph for these waves. Firstly, how exactly does one come up with such a ...
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260 views

Wave oscillation [closed]

A 2 kg block is attached to a spring for which $k=200N/m$ . It is held at an extension of 5 cm and then released at t=0 , Find a, the displacement as a function of time and b, the velocity when $...
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3k 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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131k views

How to find the phase constant? [closed]

I was given this velocity-vs-time graph of a particle in simple harmonic motion: I determined the amplitude to be $A = 1.15$ m, which Mastering Physics confirmed is correct. Then I was asked to find ...
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2answers
235 views

Harmonic Motion [closed]

A light elastic string is stretched between two points, one lying vertically below the other. A particle is attached to the midpoint of the string, causing it to sink a distance h. Assuming that the ...
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1answer
6k views

Standing Waves: finding the number of antinodes [closed]

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 ...
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0answers
15 views

Motion of the particle and resonance [closed]

A particle of mass $m$ is attached to two springs. The spring on the left has constant $k_{0}$ and the spring to the right constant $1.5k_0$, and both have null natural length. The spring on the right ...
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1answer
38 views

Thermodynamics of harmonic oscillators [closed]

I have N harmonic oscillators in thermal equilibrium at temperature $T$, $$ E(n_{1},...,n_{N})= \hbar \omega \sum_{i=1}^{N}(n_{i} + \frac{1}{2})$$ And I calculated partition function like this $$Z = \...
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1answer
95 views

How to tell if this system is doing simple harmonic motion? [closed]

Let there be 2 small bodies of same mass $M$. And they are connected by a spring and they are initially rotated by velocity $V$. So by this the spring expands and contracts. The force on the block is ...
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1answer
43 views

Can anybody tell me the difference between these two velocity?

In Waves i earlier studied that velocity of the wave is given $wa\sqrt{1-y^2}$ w= angular velocity a=amplitude of the wave y=post. of wave at any time and now when i am studying wave optics ...
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1answer
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Spring constant of harmonic oscillator [closed]

I got a task from my lecturer to solve a differential equation for a simple harmonic oscillator: $$m{d^2\vec{r} \over dt^2}=-k^2\vec{r}.$$ So far, I have managed to find this equation only in one book....
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56 views

Oscillating problems [closed]

I am practicing for my "Mechanics of continuous media" exam. There is two exercises I couldn't really do yet: A homogeneous meter rod at the 70 cm line is hooked up, and making small amplitude ...
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2answers
59 views

Determine period and angle of harmonic oscillator with $x = 2 \pi \sin(120 \pi t + 3.2 t)$ [closed]

A particle moving under simple harmonic motion has displacement $$x = 2 \pi \sin(120 \pi t + 3.2 t) \, .$$ How can I determine the period and the phase angle?
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71 views

Investigating 2D Oscillating motion

I once did an experiment into Simple Harmonic motion of a mass oscillating in 1D on a spring. I wanted to extend this into two dimensions. I can see how varying the starting offset and also ratio of ...
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2answers
2k views

Potential energy of vertical spring

I have an oscillating vertical spring with a mass attached. If I set the resting position of the mass as $x=0$ as the spring oscillates, I will have a graph like this: (source: iop.org) If I want to ...
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143 views

Simple Harmonic Oscillation of a vertical Spring

If a spring with a spring constant of k is hung vertically, and a mass is attached to it the spring will rest in equilibrium at some distance h from the springs original equilibrium length because ...
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1answer
832 views

Simple pendulm motion for larger angular displacement? [duplicate]

What will be the nature of the motion of a simple pendulum for larger angular displacement? Will that be a periodic motion? If so, will the time period increase or decrease?
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72 views

What are these constants and why do we use them in this equation?

The equation $f(t) = D \sin(\omega t +\phi)$, here the constants are $D$ and $\phi$ and they are added while deriving the given equation from $$f(t) = A\sin(\omega t) \tag{1} $$ $$f(t) = B\cos (\...
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46 views

uncoupling pertubated 2-D harmonic oszillator

I want to exactly solve a two dimensional harmonic oscillator with $$ \mathcal{H} = \dfrac{p_x^2}{2m} + \dfrac{p_y^2}{2m} + \dfrac{m\omega^2}{2}(x^2+y^2+2K xy)$$ I understand that I have to find a ...
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1answer
547 views

Wire loop oscillating inside a magnetic field (energy conservation)

Let $\vec{B}$ be an uniform magnetic field in space. I'm having problems trying to imaginate the behavior of a wire loop inside the magnetic field. First, we got that the torque $T$ will be $T$ = $\...
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3answers
2k views

Change in period of damped pendulum system [closed]

Suppose we have a simple pendulum damped by air resistance, proportional to the velocity of the pendulum. By using the small angle approximation of sin, we are able to solve a second order ...
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1answer
666 views

Simple Harmonic Motion vibration and waves

In SHM, acceleration is always in the opposite direction of the oscillating particle.But, in the case of a pendulum, when the bob is, at first, set free, it's displacement is towards the acceleration ...
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1answer
369 views

Damping on a pendulum

So I have this question where you are given a simple pendulum, and you are asked how increasing the damping will affect the frequency and amplitude, I am at a loss as the answer says that frequency is ...
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1answer
55 views

Deriving eigen values of $\hat{N}$

So let's say we have an operator $\hat{a}$ (ladder operator), where $\left[\hat{a},\hat{a}^\dagger\right] = 1$, and $\hat{a}^2 |\phi\rangle = 0$. How do I show that the eigenvalues of $\hat{N}=\hat{...
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849 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
633 views

A block falling from a height on a block suspended by spring [closed]

The block suspended by the spring is hanging freely and its mass is M. The small block of mass m is dropped on the bigger block from height h. After the small block is dropped 》》》 I want help in ...
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1answer
45 views

Alternative method for deriving $T=\frac{2\pi}{\omega}$ for S.H.M

I am trying to derive: $T=\frac{2\pi}{\omega}$ for S.H.M. I want to use the following method. A particle is at position $x=x_1$ on the x-axis. It starts with zero velocity. $x_1$ is therefore the ...
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1answer
115 views

Average value of an operator on vacuum state [closed]

I'm trying to calculate $$<0|e^{a\hat{x}^2}e^{b\hat{x}}e^{c\hat{p}}|0>$$ where $a$, $b$ and $c$ are complex numbers, $\hat{x}$ is the position operator, $\hat{p}$ is momentum operator and $|0>...
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2answers
613 views

Simple pendulum with varying mass [closed]

If i make a simple pendulum using a ball filled with water and then puncture the ball with needle making a small hole. The pendulum is then made to oscillate . The water will flow through the hole . ...
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161 views

Can anyone explain the harmonic oscillator (in context to quantum mechanics) 2.3 (Griffiths) using Taylor series?

At the end he concludes $V(x) = V''(x_0)(x-x_0)^2$. How does he get to know that the rest are $0$? How does he conclude $V''(x_0) = k$. Please try to explain in easy ways and tough vocabulary. I don't ...
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3answers
344 views

How Hooke's Law and motion equation are related? [closed]

$$F(x)= -kx = ma(x) $$ Elastic force equation I solve this differential equation to find the equation of motion: $$ -kx =m\frac{d^2x}{dt^2} $$ $$ x'' +\frac{k}{m}x=0 $$ $λ^2 = -\frac{k}{m} $ $ λ ...
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2answers
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What is the formula for max kinetic and max potential energy of a spring? [closed]

What is the formula for max kinetic and max potential energy of a spring?
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1answer
50 views

How to derive the single harmonic oscillator propagator given the ground state wave function? [closed]

The propagator is defined to be $\langle x|U(t;0)|x'\rangle$, and assume that we know the SHO ground state wave equation $$\psi_{0}(x)=(\frac{m\omega}{\sqrt{\pi}\hbar})^{1/2}e^{-m \omega x^2/2\hbar}$$ ...
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1answer
1k views

Tension in pendulum [closed]

I am asked to calculate the tension in the rope of a pendulum at (a) its initial position as well as at (b) its lowest position. $L = 3 m$ $α = 10^o$ $mass = 2kg$ (a) For the intial point I used ...
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1answer
284 views

Does "the initial phase of oscillation is 45°" mean a time dependence of the form $\sin(\omega t+\pi/4)$ or $\cos(\omega t+\pi/4)$? [closed]

A point particle of mass 0.1 kg is executing SHM with an amplitude 0.1 m. When the particle passes through the mean position, its kinetic energy is $8 \times 10^{-3}$ Joule. Obtain the equation of ...
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2answers
204 views

Spectral decomposition and a harmonic osillator [closed]

A system is described by a Hamiltonian $$H^0=\frac{p^2}{2m}+\frac{m\omega^2}{2}x^2.$$ A perturbation in the form of $$H'=\lambda \frac{4m^2\omega^2}{\hbar}x^4$$ is applied. I showed that $H'=\hbar\...
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2answers
280 views

Why is the net force maximal at maximal displacement in a suspended spring? [closed]

When at maximum displacement, the $x$ and $U$ are max., $K$ and $v$ are $0$. But why is net force max.?
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1answer
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period of a pendulum immersed in water

Does the value of $g$ change inside a dense fluid? How would the time period of simple pendulum change when immersed in water?