Questions tagged [oscillators]

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Oscillation of a cylinder hanging from a table

A cylinder is tied to another object that is moving in circular motion on top of a table. Initially the object moves at an angular velocity that prevents the cylinder from moving. If the cylinder is ...
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It's a question from a book I can't solve [closed]

A block A of mass m and length l is placed on a horizontal floor. Box B is used to cover A. The distance between interior of walls of B is (>1) and the mass of B is also m. The coefficient of ...
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2answers
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Why does general homogenous solution of differential equations modelling circuits die off after a long time?

I was reading this answer in Elecronic engineering stack exchange which said that when solving the linear second order differential equation modelling circuits having ac source. We only need to ...
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1answer
70 views

My simple pendulum has a period about 1/3 what it should be

I'm a high school science teacher, my primary degree is in Physics, so I have a solid grasp of the background. I'm running into a strange issue with a pendulum lab I had my students complete. We're ...
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1answer
40 views

Second order ODE for constant external force

Given a general ODE for damped spring with constant external due to gravity $$my'' + \gamma y' + k y = -mg$$ where $m, \gamma, k, g$ are positive. I have to show that given an initial condition, the ...
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How do I achieve 50Hz using an astable multivibrator? [migrated]

So based on the $f=1/1.38RC$ equation I came up with the conclusion that $R$ must be 69000 ohms and $C$ must be 1000uF, is this correct? And I have a side question: If I am charging a capacitor ...
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1answer
33 views

Pendulum on an accelerating train with changing length

Based on my own research, I found a general solution that can model a pendulum found on an accelerating train. The following solutions are based on small angle approximations. F=-mgsin θ F≈-mgθ, ...
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1answer
28 views

Along which axis is the moment of inertia of a harmonically oscillating body calculated?

I have been learning about oscillating bodies and recently stumbled upon physical pendulums. Now the problem is i don't understand about which axis is the MOI calculated while finding the TIME PERIOD(...
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1answer
79 views

Mathematical (simple?) vs physical pendulums

I've looked long and hard for what a mathematical pendulum is but no site clearly has the name "mathematical" pendulum but it's all over the book "Problems in General Physics" by I....
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1answer
35 views

Natural frequency mass-spring system on inclined plane [closed]

I have to find $\omega$ for this system using the forces. I have a disc $radius = R, mass = M$ By using $F=ma$, I get $mg\sin\theta - kx = m\ddot{x}$ then $$-g\sin\theta + \frac{kx}{m} + \ddot{x} = 0$...
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3answers
65 views

Pendulum attached to an accelerating train

The question I have is similar to that of the Pendulum in an accelerating train problem. Where a bob is hung from the ceiling of a train that is at rest. The train then begins moving with an ...
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1answer
38 views

Equations of the spherical pendulum in different coordinates [closed]

I am trying to derive the equations of motion of a spherical pendulum, but instead of using the angles of the spherical coordinate system $\theta$ and $\varphi$, I want to use the angles $\alpha$ and $...
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How do I separate two different creation/ann operators?

$a$ and $b$ are identical systems. The Hamiltonian is given by $H=H_a+H_b =a^\dagger_k a_k +b^\dagger_k b_k$ and these are non-interacting particles. How do I separate a time dependent operator $A(t)= ...
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1answer
21 views

Initial conditions of transient behavior of a driven oscillation

For a driven oscillation $$X_G = A_0e^{-\frac{\gamma}{2}t} cos(\omega_v t + \phi) + A cos(\omega_d t - \delta),$$ where $A_0$ and $\phi$ are determined by the initial conditions $x_0$ and $\dot x_0$ ...
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3answers
225 views

The mathemathical physics behind punching things that hang

How do you calculate the angle at which a hanging body will move when it is hit on it's hanging end?
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1answer
31 views

Difference between periodic motion vs harmonic motion vs simple harmonic motion

So , I am kind of confused about the difference between these three things: (i) Periodic motion. (ii) Harmonic motion. (iii) Simple harmonic motion It will be the best if someone showed me the ...
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27 views

Waves and simple harmonic motion

Is it possible to always assume that a wave is generated from the medium components oscillating in simple harmonic motion with same amplitude but just out of phase with each other? For example, I've ...
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2answers
18 views

Resonance of a damped harmonic oscillator under forced oscillations

Suppose we have a damped harmonic oscillator and we also apply an external force such that our system oscillates in steady state. If the frequency of my force matches the natural frequency of my ...
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0answers
7 views

Interpreting vibration graphs to find number of equilibrium points

In Coulomb damping, there is a continuous range of equilibrium points. However, from the graph above it appears that only 1 or 2 equilibrium points exist because the system is in equilibrium when the ...
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1answer
57 views

Time for critically damped oscillator to reach equilibrium?

The title says it all. With my limited knowledge of physics and math, I have no idea where to begin, as the position function I have for a critically damped oscillator, $x=e^{-\omega_0t}[x_0+(v_0+\...
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1answer
46 views

Measuring the natural frequency of a spring-mass system with the graph

On a graph of a system under a external force y = distance and x = time where the external force start at t = 0, it's easy to find the driving frequency. $$F = \frac{\omega}{2\pi}, \omega = \frac{2\pi}...
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1answer
36 views

How a pendulum accelerates?

I have learned that $-g\sin\theta$ describes the acceleration of a pendulum. But surely if a pendulum is held from a point, say this point is $a$ and another point $b$ and say suppose that point $a$ ...
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0answers
31 views

Derivation of speed of sound in (diatomic) chain using Newton-Laplace formula

I am familiar with the derivation of the speed of sound done in the style of, for example, this question: Diatomic chain and speed of sound I would like to derive that same result $$ c^2=\frac{2ka^2}{...
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1answer
43 views

Will two balls in a bowl come down at the same time?

I've been reading about pendulums and oscillators recently and I've learnt that the time period the pendulum is independent of its amplitude and we can conclude by symmetry two pendulaums at different ...
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19 views

Time period of oscillation [duplicate]

I've studied simple harmonic motion and the relation that force $\mathbf F$ is proportional to $-x$ and time period of motion. But if in some other motion, $\mathbf F$ is proportional to some other ...
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22 views

Pendulum on a moving cart that begins acceleration

I have a pendulum hanging on a cart that is travelling at constant velocity. The pendulum is oscillating about a fixed pivot. The initial movement of the pendulum can be represented by this equation: $...
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3answers
71 views

Oscillator what's the steady state?

I'm wondering what's the steady state for an oscillator. Is it a system without driving force so without external force to disturb the system? If a system oscillates without driving force can we say ...
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1answer
58 views

How to find the max angle the pendulum reaches during oscillation?

I have a pendulum that is swinging with no loss of total energy. Is it possible to find out the maximum angle, $\:\theta_{o}$ to which the pendulum reaches, based on only the following information? ...
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1answer
33 views

Calculating Phase difference

Based on the image below, you can see two waves. The black wave is phase shifted towards the left. If I know their starting positions 3$^{\circ}$ and 5$^{\circ}$ respectively for the black and blue ...
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0answers
29 views

Period liquid in a U-tube [closed]

I have to find the oscillation period of a liquid inside a u-shapped tube. All I have is the density = $\rho$, liquid length = $l$ and the section = $A$ The only way I found is by the conservation of ...
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3answers
528 views

Forced Oscillation Explained with Violin String

In this lecture on Forced Oscillations, Normal Modes, Resonances, Musical Instruments, the professor says that by moving a bow over a violin string, you expose it to a lot of frequencies. Is there a ...
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Is there a relationship between the initial length of a pendulum that is released in air, and the amplitudes half-life (defined in post)?

If I were to release an underdamped pendulum right now in earth's regular atmosphere, factoring in air resistance, is there a way to plot the motion of the pendulum using a regular function? Also, ...
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58 views

A very interesting problem on simple harmonic motion and detailed analysis of momentum and energy involved

I am a high school student and I am a little confused in a question. this is a problem from Simple harmonic motion, I have found its solutions on many places but no solution turns out be convincing ...
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2answers
79 views

Is there a way to describe oscillations without referencing trigonometry?

When studying physics, I often come across sines and cosines, and while I understand they're an elegant and useful way to describe systems with periodic characteristics, I can't help but wonder ...
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9answers
5k views

Intuitively, what actually is the cause of resonance?

Please don't explain it mathematically. I have been searching for the reason for a long time. I have watched Walter Lewin's video giving an example of resonance, but I didn't get the reason behind the ...
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3answers
66 views

Will this system undergo simple harmonic motion? [closed]

I was recently studying Simple Harmonic Motion, In which I came across a problem. It deals with small angular oscillation (a light shaking of Sphere), I extended this problem and asked my teacher ...
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1answer
34 views

What is the formula for displacement in simple harmonic motion?

I am studying SHM in my physics class right now and I often get confused with the formula for displacement. Sometimes I see the formula written as $x=A\sin(\omega t)$ and sometimes I see it written as ...
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2answers
50 views

How to calculate damping ratio or critical damping of a system with two springs and a damper (or two springs and two dampers)?

Background For a simple system where you have a mass attached to a spring and damper in parallel: We can calculate the critical damping from the equation of motion: $$mx_{tt} + cx_t + kx = 0$$ $$ms^2 ...
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20 views

Resonance curve of a Harmonic oscillator

The resonance curve of a damped harmonic oscillator has a peak at the resonant frequency $\omega_0$. If the damping coefficient $\gamma$ is more then the peak is lower, compared to before, i.e the ...
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4answers
101 views

When to use $x = A \sin (wt + p)$ and $x = A \cos (wt+p)$ during Simple Harmonic motion when we start our clock not between mean and extreme position? [duplicate]

When to use $x = A \sin (wt + p)$ and $x = A \cos (wt+p)$ during Simple Harmonic motion when we start our clock when the object is between mean position and extreme position ? I have been trying to ...
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2answers
78 views

Energy of a Forced Oscillator

In forced oscillations (steady state) under damping, the energy that the external force gives to the system is spent against the work done by the damped forces, and thus the stored energy of the ...
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3answers
66 views

Complex notation in harmonic oscillator

For a simple harmonic oscillator, $$x(t) = A \cos(\omega t).$$ We can also write $x(t)$ as: $$x(t) = C_1 e^{i\omega t} + C_2 e^{-i\omega t}.$$ Why is it necessary that the coefficients $C_1$ and $C_2$ ...
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18 views

Earth's atmosphere as an oscillator

I have read that earth's atmosphere is an oscillator because it is effectively revolving about the earth. However, this is an example of forced oscillations because the moon also effect it with it's ...
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20 views

How is the electron cloud oscillating during localized surface plasmon resonance with respect to the electromagnetic wave?

I have seen many illustrations like this for example (from Wikipedia) where the induced electric field in the nanoparticle is opposite to the one in the electromagnetic wave. This is the most common ...
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1answer
41 views

Where did the boundary conditions go in the frequency-space solution to the Green's function for a damped harmonic oscillator?

In differential equations, Green's functions are only defined given boundary conditions. In fact, you need two of them for a second order differential equation. In a lot of physics lecture notes, a ...
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2answers
40 views

Why isn't pendulums with “large” initial angular displacements not considered simple harmonic oscillators?

The tangential force exerted on a pendulum weight is $-mgsin(\theta)$. If we say that the pendulum has length L than $sin\theta$ = $\frac{x}{l}$. Then $$F_{tangential} = \frac{-mg}{l}x$$ Then why do ...
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How to derive the response function of $m\ddot x + \gamma \dot x + kx = f$?

In a lecture on fluctuation-dissipation theorem, it is stated that EOM: $m\ddot x + \gamma \dot x + kx = f$ Response function $\chi(\omega) = (-m \omega^2 + i\gamma \omega + > k)^{-1}$ However, I ...
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33 views

Clear understanding of two concepts

I have been studying about oscillation, where I get to know about its two types (i.e) Harmonic motion Non Harmonic Motion While studying about harmonic motion,I came to know that force is directly ...
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3answers
40 views

Oscillatory motion

As I was studying about simple harmonic motion(example pendulum), then I came up to a sin graph as well as a formula that is y = sin2πt/T. I then taken the example of pendulum to understand as to how ...
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1answer
39 views

Period of a circular arc shaped pendulum

The period T is equal to $2\pi/w_n$ where the natural frequency can be found from $w_n^2{\theta}+\ddot{\theta} = 0$. Since $\tau = I\alpha $, as there is no net torque about point P because gravity ...

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