Questions tagged [oscillators]

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1answer
47 views

While determining phase, is it okay to choose displacement as zero?

There was this sentence in my book on simple harmonic motion, under the section where they explained it in terms of uniform circular motion. The projection on X axis of a particle p as well as it's ...
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1answer
181 views

Oscillation of mass $m$ on a spring when another mass $m$ is added to it at equilibrium

I have a spring of length $L$ when unstretched with one end fixed to the roof. At the lower end I place a mass $m$ and drop gently so it stretches by $x_1$ at equilibrium so that $mg=kx_1$. Now I ...
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1answer
69 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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1answer
141 views

LC Circuit with a DC input

In the previous LC circuit, if we connect one end with a DC input voltage and the other with ground, what does the oscillating output wave look like? I know that if the capacitor was initially ...
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2answers
104 views

Can time period for pendulum be negative? [duplicate]

For a pendulum, a= acceleration, y= displacement, w= angular velocity, T= time period. We have →|a| = yw² →a/y = w² = (2π/T) ² →2π/T = +√(a/y) or -√(a/y) →T= + 2π√(y/a) or -2π√(y/a). Is this ...
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1answer
60 views

Is it possible to approximate the motion under a V-shaped potential as harmonic motion?

Let's assume an $xy$ plane and let there be a force field defined by the potential $$V=F_0|x|$$ Though the potential is not differentiable still its a perfectly realisable system. If we solve the ...
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2answers
52 views

How phase lag varies depending on frequency

I am going through E. Hecht's "Optics", and I am currently trying to solve some problems from the book. However, I need help with one of them. The equation for a driven damped oscillator is $m_e\...
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1answer
378 views

Logarithmic decrement in underdamped oscillations

In the picture, logarithmic decrement is defined and is explained. I can't make out the meaning. I tried searching in Google but it doesn't help. Can you explain it in a simple yet effective way ?
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2answers
587 views

Oscillations of LC Tank circuit connected to a DC Source

I have this circuit where I have connected a LC tank to a DC source through a resistor. I am not able to figure out how would this system oscillate. If I check the Voltage across C1/L1, will the ...
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1answer
137 views

Critical damping, overshooting

For an over damped system, the position is given by: $$x(t) = \frac{1}{2\kappa}e^{-\gamma\cdot t}[(\kappa\,x_0+ \gamma\,x_0 + v_0 )e^{\kappa t}+(\kappa\,x_0 - \gamma\,x_0 - v_0 )e^{-\kappa t}]$$ ...
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2answers
45 views

Why the oscillator would vibrate without a driving force?

I am going through "Optics" by E. Hecht and I think I am misnderstanding the following paragraph: $x(t) = \frac{(q_e/m_e)}{(w_0^2-w^2)}E(t) $ This is the relative displacement between the ...
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0answers
4k views

Finding the damping constant and period from looking at a graph [closed]

I want to make sure there are no holes in my logic in solving this problem. From the figure, I am instructed to determine the damping constant as accurately as possible. Here's what my thought ...
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3answers
2k views

Pendulum in elevator accelerating upwards [closed]

I know that there are already answers to this question, but I am still a little bit stuck. I know that the period of a pendulum is T = 2$\pi$ $\sqrt[]{\frac lg}$. When the elevator accelerates upwards ...
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1answer
398 views

Better understanding natural resonance frequency and simple harmonic motion

Let me see if I'm getting this understood correctly. I'm trying to make sure my interpretation of simple harmonic motion is the right interpretation, including my take on resonant frequency. Okay, so ...
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0answers
100 views

Deterministic non-harmonic motion of a single spring

Is there anything describing a spring's motion when e.g pulled and released, or pushed and released, with no mass-body attached to the spring. I.e not your usual "mass motion on a spring"-equation. I'...
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1answer
92 views

What is a phase of a waveform?

Can please someone give a simple explanation of the phase of a waveform, particularly the sine function? Also, what is the angular frequency, and how does it differ from the frequency?
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2answers
438 views

Why do all materials resonate? [duplicate]

Why do things vibrate with resonant frequencies. Why are there multiple frequencies from one impulse? ammendment: Why do chimes from bells have overtones? How to drums have overtones? What is ...
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2answers
650 views

Why does the mass of an object attached to a pendulum affect the damping?

I tested this out on a simulation (Algodoo) and found that a pendulum with a more massive object attached to it has a lower damping on its velocity. Why does this happen?
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1answer
469 views

What is radial oscillation and how is it measured?

In the context of the Earth orbiting the sun, the question of the problem is "If the radial oscillation has a higher frequency than the time it takes the Earth to orbit the sun, will the aphelion ...
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0answers
22 views

Deriving the normal force for an oscillatory system

I'm trying to wrap my head around the following exercise: 4) Consider a U-tube filled with a liquid with density 𝜌. If you blow into one of the sides, the liquid in both sides is displaced from ...
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1answer
43 views

Derivation of damped SHM velocity expression

This is from Main: Vibrations and Waves in Physics. This is a (basic) standard treatment, regarding SHM light damping and using a trial solution $x=Ce^{pt}$. Roots of p are $-\frac {\gamma}{2} \pm ...
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0answers
81 views

Frequency of an underdamped driven oscillator

Let a particular solution of the differential equation $$\ddot{x}+2\gamma \dot{x}+\omega_0^2 x=\sum_{n=-\infty}^{\infty}c_n e^{i n \omega t}$$ be given by $$x=\sum_{n=-\infty}^{\infty}\frac{c_n}{2\...
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1answer
65 views

Considering moment of inertia - why do pendula $1$ and $2$ have the same resonant frequency? [closed]

This question was given to me during a lecture. The axis of rotation is into the page, such that the pendulua all swing to the left and the right (and I think it would be obvious to note we're ...
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1answer
211 views

Determination of spring constant $k$ for an elastomer

Primary Question: How can you determine the spring constant $k$ of an elastic material? I was recently tasked with finding the spring constant for a series of elastomeric materials, the first of ...
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0answers
85 views

Massless Electrons and Effect on Graphene Mass

I've read that electrons in graphene can travel masslessly, due to the effect of the graphene crystal around them. I'd also read that the application of an electric field can change this behavior and ...
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2answers
129 views

A particle subject to a potential of the form $V(x)=V_0\vert x \vert$ [closed]

A particle is moving in a potential $V(x)=V_0\vert x \vert$. I need to get the angular frequency and the period of the movement of the particle. This is what i have done. The equation of motion is $...
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3answers
538 views

Can we guess the periodic/aperiodic nature of motion from the equation of motion?

The equation of motion of a pendulum with a bob of mass $m$, and hanging by means of a massless thread of length $T$ is given by $$\ddot{\theta}+\frac{g}{l}\sin\theta=0,$$ and that of a damped one-...
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1answer
264 views

Ordinary vs. Angular Frequency in SHM

I seem to be puzzled by the importance of using angular frequency $\omega$ as the frequency scalar to the mathematical model of Simple Harmonic Motion rather than merely using $f$, and by $f$ I mean $...
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1answer
105 views

Modeling physical pendulum as a simple pendulum system

Before you continue, please excuse my English. It is not my native language.How can I change the physical pendulum system into the simple pendulum system?Should I just design the length of thread or ...
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3answers
2k views

Is the displacement of a driving oscillator in phase with the driving force?

In a set up such as the following: I have read in many places that below resonance the driving force is in phase with the harmonic oscillator. I have also read that the driving oscillator is in phase ...
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6answers
2k views

Simple Pendulum Why Generalized Coordinate Always Angle?

When writing the equations of motion for the simple pendulum, why do textbooks always choose $\theta$ to be the generalized coordinate? The force of gravity is in the y-direction so wouldn't it be ...
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2answers
1k views

What is the oscillation frequency of a buoyant cylinder?

Suppose a cylinder sits upright in "dry water" (zero viscosity). The cylinder has half the density of the water, and we'll ignore the dynamics of the atmosphere. If I push the cylinder down some past ...
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2answers
157 views

Significance of the word 'linear' in linear harmonic oscillator

In my book Advanced Acoustics there is a line- A particle undergoing SHM is called a linear harmonic oscillator If I say that the word linear is used for the 2 reasons- The motion of the particle ...
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1answer
55 views

Is there a relation between phase plane and complex plane?

The only occurrence I see complex numbers used in dynamical systems is to analyse the eigenvalue $\lambda$ of the linearised approximation to determine the characteristics of equilibrium points. ...
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0answers
98 views

Solvable model with harmonic oscillator

I need help with a mathematical physics question. I have given the following system: A spin is coupled to a single harmonic oscillator mode with Hamiltonian $$H=(\epsilon/2) \sigma_{z} + \omega\, a^{...
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1answer
225 views

Varying amplitude of beats

Why is the product of 2X and cosine delta t divided by 2 is the varying amplitude and not the other 2X and cosine function?
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1answer
233 views

Euler-Bernoulli equation for a cantilever strained by a force

I'm trying to model an experiment where a cantilever, fixed at one end, is oscillating under an applied force at the free end. Specifically, I'm focusing a laser on a rectangular cantilever and ...
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1answer
253 views

Will the amplitude of a undamped forced oscillator keep increasing till infinity?

It seems like a straightforward answer but I still need confirmation. Can someone mention diagrams as well? Because I saw that there are three possibilities depending on initial and vibrating ...
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1answer
122 views

What branch of physics covers most of these questions?

I am close to finish the book Vibration and Wave by French, and I would like to know which branches of physics can answer these groups of questions: Defining questions: Can a periodic event be ...
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1answer
1k views

How to plot forcing ocillation with damping correctly? [closed]

The forced oscillation with damping is described as $$\frac{d^2x}{dt^2}+\gamma\frac{dx}{dt}+\omega_0^2x=\frac{F_0}{m}\cos{\omega t}$$ Its solution is $x=A\cos{(\omega t-\delta)}$, with $$A(\omega)=...
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1answer
609 views

Time period of a rigid rod pendulum has same value at two different point of suspension, why?

While solving the problem of the rigid rod pendulum I figured out that when the point of suspension is at the end of the rod and and at $x = \frac{l}{3}$ from same end, time period of oscillation has ...
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0answers
99 views

Oscillating waves on a water stream

I observed something which I've never seen before. We left the tap open and the water stream was flowing in a particular pattern. When we placed a beaker under the water stream, the pattern ...
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1answer
1k views

What are practical uses of over-damping? [closed]

We have been given this task of preparing some small research on critical damping and comparing its behaviour and uses with over-damping. I am done with everything else but have been unable to find ...
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2answers
95 views

How well does this solution model damping? [closed]

I was wondering if someone could please tell me why this below solution models damping well? In particular its amplitude and frequency of the damped oscillation. $$y=e^{-λt/2m}[A\cos(Λt)+B\sin(Λt)],$$...
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4answers
105 views

Does it make sense to talk about a frequency when we deal with damped oscillations?

I'm solving a problem in which there is a damping force in the form $F = -bv$. The question asks for the "frequency of oscillation", but since it is a damped oscillation I am confused, because I think ...
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1answer
121 views

Meaning of complex oscillation equation

I have the problem of a dampened harmonic oscillation (more concrete a "Pohl wheel" (here is an illustration of it)) whose motion is given by the following differential equation $$J\frac{d^2 \alpha}{d ...
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1answer
58 views

Removing Free Oscillations

A forced oscillator can be described by the equation $\ddot{x} + \omega^2x = F(t)$. The solution of this equation will have a free and forced solution, with the free solution being just $x(t) = Ae^{i\...
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1answer
259 views

Synchronized oscillations

Please I'm a little confused about this. When are oscillations said to be synchronized? Is it because they vibrate at the same frequency or because they are in phase? Got a question with both options.
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2answers
91 views

Driven oscillator solution intuition

For the sinusoidally driven oscillator given by: $$m\ddot{x} + b \dot{x} + kx = F_0 \cos(\omega t)$$ or $$\ddot{x} + 2\beta \dot{x} + \omega_0^2x = A \cos(\omega t)$$ The particular solution is: $...
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1answer
768 views

Taylor expansion of potential energy

According to the book "Applied quantum Mechanics, Anthony Levi", The Hamiltonian of a monatomic linear chain is given by: The first term on the right side comes from the sum of the kinetic energy of ...