Questions tagged [oscillators]

A mechanical or electronic system or device that works on the principles of oscillation, that is a periodic fluctuation between two things based on changes in energy. These range from abstract models such as a harmonic oscillator to electrical devices such as an LC circuit.

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Analyzing the ratio of the period of a small and large angle oscillation

I'm trying to understand how the angle of an oscillation really affects the period of a given system. For angles where $\theta_{0} \ll 1 \text{ rad}$, the approximation is well known as: $$ T_{small} =...
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Zero gravity mathematical pendulum [closed]

What will happen if a mathematical pendulum will be in a zero gravity condition? And the same question for a spring pendulum.
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Why we want the string to be massless in the ideal model of simple pendulum?

I couldn't think about a reason why the string must be massless. Wouldn't the assumption that the air resistance is negligible, the angle $\theta$ is small and the string is non-stretchable suffice ...
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What is the difference between amplitude and phase angle for a pendulum?

I understand the definition in terms a plain trigonometric function, such as $A\cos(\omega t+\phi)$. The amplitude is half of the distance between peak and bottom, and the phase angle* is how the ...
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Analysis of damper having mass

How to do analysis of a non ideal viscous damper (damper having mass)? How to find out an equivalent system for it?(having a ideal damper)
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When will two pendulums be in phase with each other?

Two pendulums with different frequencies released at the same time, when will these two pendulum be in phase? From what I know, the period of pendulum at small displacement is not affected by its ...
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Velocity amplitude and velocity resonance In Forced Harmonic Oscillator

In the forced harmonic oscillator the velocity of the oscillator is given as - $$V=Ap\cos(pt-\varphi)$$ where , $p$= the driving angular frequency, $A$= amplitude of the forced harmonic oscillator. ...
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The spring-pendulum with a spring of non-negligible mass

In Goldstein's Classical Mechanics, 3rd edition, Chapter 1, problem 24, point (d), I am confused as to why the authors would suggest the use of an analytic computer program to supply the answer. The ...
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How do museums keep Foucault’s pendulum going constantly?

How exactly do they keep the pendulum going with out affecting the direction it travels? As much detail as possible please.
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What is the actual significance of the logarithmic decrement?

I know there is a similar question, but it does not clear my doubts on what the actual meaning of logarithmic decrement in damped harmonic oscillations is, and what the need to discover this was. ...
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Damped harmonic motion initial conditions

I was reading Halliday's section on Damped Simple Harmonic Motion, which stated that this equation: $$-b\dot{x} - kx = m \ddot{x}$$ Is the differential equation that dictates the displacement of the ...
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Why is over-damping non-oscillatory?

I have read that the during overdamping the damped forces or the resistance to movement of an object in S.H.M is so high that if the object is displaced from ita mean position then it returns to it ...
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How much does string material elasticity affect tension at pitch for a stringed instrument?

In introductory physics classes, we see the simple string oscillator equation, which can be used to estimate the string tension at pitch for a stringed instrument. However, the equation assumes an ...
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Distance Between the Point Masses in a Pair of Coupled Pendula [closed]

Here is an embarrassingly simple problem, which for some reason I can't figure out. You can also find my solution attempt here. Two point particles of mass $m$, a pair of identical rigid rods of ...
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Past prediction of a damped harmonic oscillator (a follow-up of a previous question)

Consider an ordinary differential equation (ODE) of a 1D damped oscillator of the form $$\ddot{x}+\gamma\dot{x}+\omega^2x=0.~~(\omega^2,\gamma>0)$$ I want to know if this ODE is reversible i.e., ...
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How does the load on the tip a cantilever affect how long it continues vibrating after release?

I'm considering a situation in which a load is applied to the tip of a cantilever. After the release of the load, the cantilever oscillates, but due to an energy loss to the environment (which I think ...
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Polarity of induced EMF in an LC oscillator

The image given belongs to my textbook (NCERT Grade 12, Chapter-7, Alternating Current, Pg No 255): For your reference, this is the paragraph adjacent to the picture. I believe that the polarity of ...
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Modes of vibration of triatomic molecules

$$\omega=0,\sqrt{\frac Km},\sqrt{\frac{K(2m+M)}{Mm}}$$ There are three modes here but actually triatomic linear molecule have 4 vibrational modes (e.g. CO2). So where does that remaining one mode? ...
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Damped oscillations of galvanometer

The magnet inside a galvanometer is concave, so we get rid of the $\sin\theta$ factor in the magnitude of the torque experienced when there is a current in the coil. So: \begin{equation} \tau=NSB \end{...
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How to find frequency response of a damped spring mass system using the Laplace transform

I would like to find the frequency response of a spring mass system of multiple degrees of freedom by using the Laplace transform. I think I know how to do this with one mass oscillating, however I ...
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How long will it take for a dampened spring to reach a certain point?

I've written a spring simulation for a UI in JavaScript, and everything is going great, users are able to throw UI elements all over the place and have them slide right where they need to go with a ...
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2 masses, 3 spring system [closed]

I came across this problem in normal modes of oscillations. Now I tried doing it this way: The potential energy of the system should be $$ V=\frac{1}{2}K(x^2+y^2)+\frac{1}{2}K'(x-y)^2$$ and the ...
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The physics behind a "roly poly" toy [closed]

What is the physics behind this toy?If we tilt it by any angle which force is causing it to come back?
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Coupled Oscillations: no beating effect

Consider the famous coupled oscillation problem of 2 spring pendulum: In a special case the solution can be given as follows: $x_1 = \displaystyle \frac{C_1}{2}\,\cos(\omega_1\cdot t)+\frac{C_1}{2}\,\...
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Total energy of an underdamped harmonic oscillator

I am trying to find the total energy of an underdamped harmonic oscillator, where $\gamma << \omega_0$, whose displacement as a function of time is: $$y(t)=y_0e^{-\frac{\gamma}{2}t}\cos{(\...
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How to find equation of motion of the bob in this situation? [closed]

Imagine a ball is travelling in a bumpy road like the graph $\sin x$ (I'm using $\sin x$ just as an example, it has no significance in the question I guess). So, a ball is travelling in this way and a ...
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When we talk about natural frequency of an object in the context of resonance, what exactly is vibrating, the electrons or the entire atoms?

And how exactly do objects acquire "natural frequencies"? Is it due to the temperature and the lattice structure (the type of bonds they form with other atoms)? And thus, is resonance just a ...
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Modelling Forced Oscillations with a Single Trigonometric Function

In a physics book I came across the following solution to a differential equation modeling forced, damped, oscillating motion: $$x(t)=A\cos(\omega t+\phi)$$ where $$A=\frac{F_0}{\sqrt{m^2\left(\omega^...
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Why does the Time period of a simple pendulum in a lift accelerating upwards change?

[I know this question probably has multiple duplicates. I have seen answers to one question already but wanted to know a bit more] Edit: Suppose I am in a lift carrying a simple pendulum by holding ...
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Solution to pendulum differential equation

In a chapter on oscillations in a physics book, the differential equation $$\ddot{\theta}=-\frac{g}{L}\sin(\theta)$$ is found and solved using the small-angle-approximation $$\sin(\theta)\approx\theta$...
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How to solve SHM questions using Taylor's Series? [closed]

Q) A point particle is acted upon by a restoring force $-kx^3$. The time period of oscillation is $T$, when the amplitude is $A$. The time period for an amplitude $2A$ will be (A) $T$ (B) $T/2$ (C) $...
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Why is it possible for us to "hear" acoustic phonons, but not optical phonons?

The name itself suggests that we can hear acoustic branch of phonon modes (and not the optical branch), but other than that I do not see any reason whatsoever why we are able to hear them. In order to ...
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Trying to prove the wave equation from circle

Imagine one of the point in the wave. It is in oscillation. So its displacement can be written as $Y = A\sin(\theta)$ where $\theta= \omega t$. $$Y(t)=A\sin(\omega t) \tag{1}$$ Time for one wave ...
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Why does resonance take place? [closed]

Resonance takes place when external driving frequency equals the natural frequency of an object. I know every objects have their natural frequency. But I can't see everything vibrating on its own, ...
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Is the drag coefficient the same thing as damping coefficient? Can I find the drag coefficient using the data of a damping oscillating sphere?

I am currently working on a lab experiment to find a relationship between the diameter of a sphere and its drag coefficient. I will be using a spring-mass system that oscillates vertically and then ...
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Is damping rate of a pendulum dependent on the number density of the gas?

Robert Boyle in 1660 conducted experiments where he pumped air out of a vessel with a swinging pendulum. He discovered that the damping rate of the pendulum is independent of the number density of the ...
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How Ultrasonic diffuser work?

i have studied A2 physics where i have learnt resonance and evaporation, i wondered how the ultrasonic diffuser work. my inital thought was that i guess water have it's own natural frequency, the ...
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How to find the angular frequency of a simple pendulum using this method?

I am trying to derive an equation for angular frequency of a simple pendulum. Since the torque on the bob is only due to the horizontal component of mg, I can say that, $$ -mg(\sin\theta) l = \tau$$ $$...
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Is period of an oscillatory motion constant? [duplicate]

suppose a body is moving back and forth about a mean position in irregular intervals of time. Is this motion is an oscillation or not?
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Help to understand this equation $\frac{dw}{d\omega\,d\Omega} = \frac{1}{4\pi\epsilon_0} \frac{|p|^2\sin^2\!\theta\>\omega_0^2}{4\pi c^3\gamma^2}$

I'm looking for the name of this equation. $$\frac{dw}{d\omega\,d\Omega} = \frac{1}{4\pi\epsilon_0} \frac{|p|^2\sin^2\!\theta\>\omega_0^2}{4\pi c^3\gamma^2} \left[\frac{\gamma^2/4}{(\omega-\omega_0)...
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Unable to understand waves [closed]

I am unable to understand what actually is a wave. A google search gives the definition -In physics a wave can be thought of as a disturbance or oscillation that travels through space-time, ...
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Interpreting physical meaning of normal modes

What really is a normal mode? Maybe it's because of my teachers but I find it really abstract. I know that "numerically" corresponds to the eigenvectors of the equation $\ddot{X}= -M^{-1}KX$ ...
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Why does the gyroscope oscillate a little when it just starts to precess?

I was reading up on why before starting the precession the gyroscope "goes down a little", (Link at the bottom). In this paper, while looking at the graphs I observed that before reaching ...
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What happens after steady-state forced oscillation when there's no force?

What happens when a steady-state forced oscillation stops being driven by a force? Does it inherit the frequency or it becomes a natural frequency? If the oscillation is damped, would it become the ...
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How is harmonic motion (specific and not a special case) different from periodic motion? [duplicate]

I have seen written in many books that a motion that repeats itself after a specific time period follows periodic or harmonic motion. However I know for a fact that damped harmonic motion cannot ...
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Oscillator problem [closed]

A material point of mass $m$ is elasticly connected to the origin of coordinates. Communication energy: $U=(k/2)r^2$, $k$ - coefficient of elasticity of the bond; $r$ - distance to origin. The point ...
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Pendulum Tuned Mass Damper - Mathematical Relationship between Mass and Damping Ratio

I am doing an experiment where I built a test tower with a pendulum to act as a tuned mass damper, similar to this picture below: I want my independent variable to be the mass of the pendulum (which ...
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Why is a phase shift through a time delay not used for damping in vibration dampers?

Why do oscillation dampers use signal conversion through a sufficiently massive electrical circuit (with resistors, capacitors, diodes) to create antiphase, instead of simply shifting the signal in ...
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Trouble finding the matrix form of potential energy in small oscillations (Goldstein linear triatomic molecule example)

I'm currently trying to learn small oscillations, I kind of comprehend the general theory, but I'm having hard times finding the matrix forms of the potential and kinetic energy. I have been following ...
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What is the difference between beats and wave packets?

What is the specific difference between beats and wave packets. According to my book both are the formed by superposition of two waves having slightly different frequencies

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