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Questions tagged [oscillators]

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1answer
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Application of linear constant coefficients ODE of the second order [on hold]

I've asked this question in math forum. Apparently this question is not welcomed there. So maybe here I can get a proper response. Consider ODE in the form of $$y''+ay'+by=f(t)$$ where $a$ and $b$ are ...
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1answer
18 views

“Monochromatic” vs. “Impulse” Force (What are the meanings of these terms?)

In a paper I am reading (linked below), the following is stated: The transient motions of the sphere and the gas bubble in the elastic, incompressible, inviscous medium are investigated in response ...
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0answers
27 views

Position of mass experiencing SHM about its equilibrium [on hold]

A mass of 10g is suspended from a spring whose spring constant is 100N/m. The mass is pulled down so that the spring is extended by 10cm and then released so that it describes simple harmonic motion ...
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1answer
25 views

Damped mechanical wave

a string with density $\rho$ and tension $T$ is bound at it's two ends at $x=0$ and $x=L$. there is a force acting on the string proportional to the velocity $F(x,t)= -2\gamma \rho \dot \psi(x,t)$ ...
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2answers
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Professor and textbook disagree on frequency at which a pendulum oscillates

We had a guest lecturer today who told us that the frequency at which a pendulum oscillates is $\omega=\sqrt{mgL/I}$. However the textbook states that is $\omega=\sqrt{g/L}$. Why the discrepancy?
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1answer
36 views

Harmonic oscillators in fluids and driven oscllations

If given a normal spring/mass system and letting the mass oscillate in a fluid say water, would it be possible for the motion of the fluid, if the fluid is moving to create a driven oscillation and ...
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23 views

Question on dipole radiators

Two dipole oscillators are situated with their centres in the same horizontal plane as the detector and the line of vibration is vertical. If oscillators are 1/4 wavelength apart and are 90 degrees ...
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1answer
31 views

Why is the tension in a pendulum string highest when it is at the mean position?

Why does the string of a pendulum have max tension when it is at the mean position?
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Double pendulum dynamics

It was said to me that for the 2D double pendulum $\ddot x_i=-\omega_i^2 x_i$, the potential could be modeled by $U=\sum_i \omega_i^2 x_i^2$ but just for small oscillations. So is there another form ...
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2answers
47 views

Impedance Matching in a String

I was reading 121st page of HJ Pain's Vibrations and waves and I saw this with the derivation of impedance matching on a string :- The conditions derived were: The impedance of coupling string be ...
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1answer
63 views

What is an anisotropic harmonic oscillator?

I can't find any explanation of it anywhere in the internet. How is it different from an isotropic harmonic oscillator?
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1answer
35 views

Forced Oscillations and Complex Representation

An oscillating force $F \cos \omega t = \Re\{Fe^{i\omega t}\}$, where $F$ is real, is applied to a mass $m$ on the end of a spring with spring constant $k$. The displacement, $x$, of the particle can ...
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1answer
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Interpreting derivatives

So we have a function such that the distance moved by a particle (say $s$) is proportional to $sin(Ct)$ where $C$ is a constant. Now i needed to show that the rate of change of velocity is directly ...
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Derivation of an eletrical signal propagation

I am currently undergoing a physics course about the physics of waves and vibrations ( actually following "The physics of vibrations and waves" from H.J.Pain) and I came across the coupled oscillators ...
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2answers
69 views

Significance of the complex component in the underdamped harmonic motion equation [closed]

The following differential equation represents the motion of a body of mass $m$ and displacement $x$ from the mean position, that is attached to a spring of force constant $a$ and viscous damping ...
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2answers
35 views

Do we need a small displacement to create a oscillatory motion on the spring?

Do we need a small displacement to create a oscillatory motion on the spring with a mass attached to it? Whats the limit of the displacement that we can give initally to create a oscillatory motion? ...
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3answers
70 views

Oscillator with decaying restoring force

Suppose a system that is described by the equation of motion: $$ \ddot{x} = -k\cdot x\cdot \exp\left(-\frac{t^2}{2\sigma^2}\right). $$ (For example a spring with decaying stiffness.) I'd like to ...
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3answers
48 views

Contradiction on Oscillating Mass [closed]

A bead is oscillating in horizontal direction as shown in the figure, our aim is to find the angular frequency of the oscillating bead First, we can write the potential as: $$V(l)=\frac{1}{2}k\cdot l^...
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1answer
34 views

Overdamped RLC circuit

I have a series RLC circuit with an equation: $$\frac{d^2I}{dt} + 2\alpha \frac{dI}{dt} + \omega_0^2 I = 0$$ (No outside sources affecting the circuit, only some $I_0$ was in the circuit at the ...
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2answers
58 views

Why does the length of a pendulum cause different natural frequencies of pendulums in Barton's pendulum?

In Barton's pendulum, the pendulum with string that is the same length, L, as the brass bob (source of driving frequency) has natural frequency equals to the bob's driving frequency. The pendulum ...
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1answer
24 views

Why is $Q$ factor an important quantity for electrical oscillations transmitting radio waves?

My textbook says that "$Q$ factor is an especially important quantity for electrical ossicilations trasnmitting radio waves. When selecting radio and television stations it is essential that the ...
2
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2answers
92 views

Exact equation of exponential curves of underdamped harmonic motion

I was studying the underdamped harmonic motion and got curious about the fact that the decreasing exponentials $\pm Ae^{-\gamma t}$ are good approximations only for light damping $(\gamma<<\...
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3answers
81 views

Why do lighter pendulums come to rest faster than heavier ones?

I've been reading this website, which stated: All pendulums eventually come to rest with the lighter ones coming to rest faster. I have been taught the mass of a pendulum does not affect its ...
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2answers
64 views

What causes clock drift in Quartz oscillators?

Usually, computer seem to use Quartz oscillators. In contrast to atomic caesium clocks they seem to have a relatively big drift and thus we need protocols like NTP to correct them. What causes this ...
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0answers
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Determining the most likely force constant for a one dimensional lattice of atoms

I am confused about a homework question which asks us to find the most likely value of the force constant for a 1-D lattice of atoms with alternating species of mass $m$ and $5m$. I'm given that the ...
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1answer
50 views

Why consider only real part when summing several simple harmonic motions?

I have been studying vibrations and I stumbled upon the overlapping of simple harmonic motions. Consider the case where the number of oscillators $n$ is $n \gg 1$, all of them have the same angular ...
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1answer
35 views

Damped oscillations and generalized friction

I'm reading damped oscillations from the book Classical Mechanics by Landau and Lifshitz, quoting from the text - "There exists, however a class of problems where motion in medium can be ...
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2answers
54 views

Why the resultant spring constant different in the following two cases?

In these two cases in the first case my book The Physics Of Waves And Oscillations by NK Bajaj says: That the restoring force exerted ...
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2answers
57 views

Forces on piston

When we heat any container containing a gas fitted with a piston, a part of the heat energy increases its internal energy and the rest does work on the piston. But when the gas does work the piston, ...
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1answer
26 views

Large Damped Harmonic Oscillator misunderstanding

So I'm confused, here with what is highlighted. When the book says of "order $1/y_-$" you will reduce the displacement by a factor of $1/e$. Does of order mean when the time is equal to $1/y_-$, if ...
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3answers
52 views

How LC oscillator is used for generating signals?

I have been trying to understand some practical applications of LC oscialltors and I dont seem to find much information available on net. One consistent application that I see is "LC circuits are used ...
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1answer
22 views

Damping in a stick-slip model

Usually the spring/block stick-slip models also include a damper. eg: https://nptel.ac.in/courses/112102015/10 I don't really understand the purpose of the damper. What does it represent? Also, ...
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2answers
51 views

Do meaningful bifurcation diagrams exist for systems described by vector fields on circles?

I've been reading about the vector field on a circle, and how it's been used to describe stable points for periodic motion. I have also read about how bifurcation diagrams describe changes in ...
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1answer
66 views

How resistance in coils affects the damping of oscillations of a magnet through them

I performed an experiment where I connected a magnet to the end of a spring with the north side on the bottom. The magnet at the tip of the coil was aligned to pass through a column of coils of about ...
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1answer
48 views

Why does $g$ show up in the frequency of this oscillation?

The problem diagram is given in the picture below: Having looked at this question Why does the acceleration $g$ due to gravity not affect the period of a vertically mounted spring? something troubles ...
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2answers
792 views

Pendulum period [duplicate]

In plane pendulum problem, we can calculate its period using elliptic integration. In SHO problem, we use approximation such that $\theta\ll 1$ and get the period, $2\pi\sqrt{l/g}$. Is there another ...
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0answers
16 views

Does it make sense to say that signals are ordered? That e.g. for $a < b$, $a$ Hz < $b$ Hz?

Does it make sense to say that signals are ordered? That e.g. for $a < b$, $a$ Hz < $b$ Hz? While numerically it might seem reasonable, physically I don't understand what sense would it make to ...
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2answers
99 views

Can photons oscillate?

If you fired a laser at the perfect angle at a mirror (for either mirror setup), and then quickly moved a mirror to replace the laser, will the light oscillate between the mirrors, as shown in the ...
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0answers
27 views

Breaking spaghetti and conservation of energy [duplicate]

For the past few days there have been news about scientists solving the old problem of bending a piece of spaghetti and breaking it into exactly two halves. Earlier it was already determined that the ...
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1answer
107 views

What is the effect of mass on resonance amplitude?

When a system is undergoing forced oscillations, why does reducing the mass of the system cause the frequency response curve to shift downwards? I encountered this problem in a practice paper, but I ...
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0answers
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What kind of oscillatory motion is going on in case of tune mass dampers during seismic movements?

During earthquakes, the Tuned mass dampers hanging from ceiling is undergoing continuous oscillatory motion. But what kind of motion is it? Damped harmonic oscillation or a forced oscillation or a ...
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1answer
39 views

Energy of classical Inverted Harmonic Oscillator

Quick one. Does the energy of inverted harmonic oscillator $$H(x, p) = \frac{p^2}{2} - \frac{x^2}{2},$$ remain conserved?
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3answers
211 views

How can a pendulum have amplitude greater than $\pi$?

How can a pendulum have amplitude angle greater than $\pi$? I've been reading about phase plots, which are graphs of the $\frac{d\theta}{dt}$ on the $y$ axis and $\theta$ on the $x$ axis, shown below. ...
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1answer
56 views

Oscillation period of an ideal pendulum (help with differential calculus)

I'm a first year physics major student, and this is my first question here. It's a well known fact that ideal pendulums with the same gravity acceleration and same length have the same period, now, I'...
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2answers
32 views

Oscillation period of a hard stick hung at both ends

Hi all, Does anyone know how this set-up will affect the oscillation period of the system? We have been measuring using timer and this set-up always yields longer period than standard pendulum ...
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1answer
40 views

Phase shift of damped mass on spring with moving source [closed]

I have a setup with a moving (upwards, downwards) board on which there is a spring mounted on the edge. The spring has a mass $m$ on its end and is damped in some sort of liquid. What methods could I ...
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1answer
59 views

Why are oscillations so ubiquitous in nature? [duplicate]

I'm aware that you can always approximate a potential by a quadratic term. But is this the most 'fundamental' reason for the pervasiveness for oscillations?
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1answer
32 views

A different kind of damped harmonic motion

I've read about damped harmonic motion in Feynman's lectures Volume 1. The characteristic was that the damping force was directly proportional to velocity. Is there a kind of damped motion in which ...
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1answer
35 views

Direction of friction for damped harmonic oscillator

When we study motion of springs, the force of damping(friction) is sometimes opposite to spring force (while returning to the equilibrium) and othertimes spring force is in the direction of friction ...
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1answer
109 views

Fourier Series Analysis [duplicate]

Can anybody explain this paragraph from the chapter " Fourier series and transform " of the book by M l Boas? "If you strike a piano key you do not get a sound wave of just one frequency . ...