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1
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2answers
67 views

Eigenvalue physical meaning [on hold]

What is the physical significance of eigenvalues or eigenvectors?? Please try to explain in very simple language simple harmonic oscillator , potential well could you support your answer by ...
0
votes
1answer
38 views

Lagrangian mechanics - small oscillations around equilibrium diagonalization

In my analytical mechanics class, we have been taught that normal modes of small oscillations around equilibrium are given by the solution of $$ p(\omega) = \det(K-\omega^2M) = 0 $$ Where $K_{ij} = ...
2
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0answers
23 views

Coulomb's static friction in multidimensional case - decide which mass begins to move

Consider a system of N coupled oscillators, under the effect of elastic forces, damping, dynamic and static friction and an external force; for simplicity, let's suppose $N=3$. The friction model is ...
0
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1answer
28 views

Tension in a vibrating loop

Consider a super basic 1D vibrating string, with standing waves on it. The string has length $L$, and the wave propagates at a velocity $v$. The fundamental frequency $f_1$ is given by $$f_1 = ...
0
votes
1answer
31 views

How can I derivate the solution of the under-damped harmonic oscillator?

The equation is $$ m\ddot x =-k x -\gamma x$$ Multiply by $1/m$ we get: $$ \ddot x=-\omega_0^2x - \beta x $$ We use the ansatz $x(t)=e^{\lambda t}$ So for the $\lambda_{1,2}$ we get: $$ ...
3
votes
5answers
98 views

A conceptual doubt regarding Forced Oscillations and Resonance

While studying about the Resonance and Forced Oscillations, I came across a graph in my textbook that is given below:- Now, the author writes As the amount of damping increases, the peak shifts ...
3
votes
3answers
113 views

How can $F_0\cos\omega t$ change to $F_0e^{i\omega t}$ in driven oscillator equation?

I have one thing that confuses me on deriving the solution for the Linear Forced Oscillator. Suppose we have the equation as $$ma + rv + kx = F_0 \cos \omega t$$ What confuses me is when the driving ...
0
votes
2answers
47 views

$Ae^{\mathrm{i}\omega t}$ assumption for oscillating systems (formal & intuitive)

When we obtain a system of ODE's for $n$ masses connected with springs (or otherwise obtained by small amplitudes approximation), the next steps are usually assuming a solution in form $Ae^{i\omega ...
0
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0answers
17 views

Diagonal patterns in a Chladni plate experiment [duplicate]

I am an undergraduate student that's taking physics classes and have been assigned a seminar concerning Chladni figures. I understand the theory behind it, the standing waves in 1D and 2D, Bessel ...
3
votes
1answer
44 views

What is the source of the discrepancy in my period-amplitude graph?

I was taught at school that the formula for period of a pendulum is $T=2\pi \sqrt{\frac{l}{g}}$ Later I found out that this is only an approximation valid for small angles and the accuracy of this ...
1
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1answer
30 views

Oscillating block amplitude change when 2nd mass added [closed]

There is a oscillating block with amplitude $A$ and mass $M$. We add a mass $m$ with zero velocity and vertically.when the block is in this two conditions: ...
1
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2answers
64 views

How can a harmonica make some different sounds?

My first post: I have found an interesting harmonica here. So, I tried to know more about harmonica. And, I have read this article , in which the author doesn't mention the physical calculation, ...
0
votes
1answer
64 views

In an RLC series circuit on resonance, how can the voltages over the capacitor and the inductor be larger than the source voltage?

Consider an RLC circuit in series, of the form If the source drives the circuit in AC at the resonance frequency $\omega =1/\sqrt{LC}$, the peak-to-peak voltages on the capacitor and the inductor, ...
0
votes
0answers
16 views

Why are sinusoidal waves so natural? [duplicate]

My question is, why do very simple systems like a spring with a mass attached to it, or an LC oscillator, or a string, all vibrate or oscillate with a sine wave? I fail to see the "circle" or the ...
0
votes
0answers
22 views

For series LCR oscillations (resonance), why does current have to be maximum?

I learned about a year back that systems will go into oscillations with high amplitudes if the frequency of the forced oscillations coincide with the natural frequency of the system leading to ...
0
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1answer
37 views

Prove that $n$ degrees of freedom leads to $n$ normal modes

I have probably missed that during my studies. I intuitively know (but then I might be wrong in some detail, that's why I am asking), that $n$ degrees of freedom in oscillating system leads to $n$ ...
1
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0answers
60 views

Odd question on potential energy [closed]

A particle with mass $m$ is acted on by a conservative force and moves along a path given by $x = A\cos\omega t$ and $y = B\sin\omega t$, where $A$, and $B$ are constants. Find the potential energy of ...
-1
votes
1answer
55 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 ...
0
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2answers
60 views

Magnitude of tension in a bent string

I understand tension in a straight string as a reaction force to a weight, which acts along the string, ultimately resulting from the attractive forces between the constituent particles of the string. ...
0
votes
1answer
40 views

How to explain the motion of these pendulums? [duplicate]

Got very interested recently in a video I saw running thru my feed: https://www.facebook.com/PortalAECweb/videos/913996365374257/ Well, I got very intrigued about the physics of it and wanted to ...
1
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3answers
101 views

Simple harmonic motion versus oscillations

I want to see whether certain oscillations in my daily life, such as the oscillation of violin strings when plucked, are simple harmonic motion or not. Can we identify whether an oscillation is simple ...
0
votes
1answer
120 views

Why is the energy stored in a driven oscillator equal to the product of friction dissipated power $P_\text{fr}$ & decay time $\tau$ at resonance?

This is an excerpt from Waves by Frank S Crawford Jr. [...] At steady-state the time-averaged power must equal the time-average of power dissipated by friction. The instantaneous frictional force ...
0
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1answer
72 views

Motion of string fixed at both ends

I was reading about the Fourier analysis from Waves by Frank S Crawford Jr. But I got trapped at the very beginning; this is the excerpt that troubled me: Motion of string fixed at both ends. ...
1
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0answers
25 views

What is the role of the hyperfine interaction in singlet-triplet transition of spin correlated radical pairs?

I don't really understand the hyperfine structure. I understand, that the magnetic dipole moment of the nucleus interacts with the spin of an electron, causing a split between the energy levels of ...
0
votes
1answer
67 views

An overdamped oscillator with natural frequency ω and damping coefficient γ starts out at position x0 > 0 [closed]

An overdamped oscillator with natural frequency ω and damping coefficient γ starts out at position x0 > 0. What is the maximum initial speed (directed toward the origin) it can have and not cross the ...
0
votes
1answer
85 views

Can friction change the resonance frequency of a system?

I am simulating the transient response of a mass-spring-damping system with friction. The excitation is given in the form of a base acceleration. What I am not sure about is: can the friction change ...
0
votes
0answers
21 views

How to determine time of dephasing?

Let's assume that I have an oscillating value A. After some time the oscillations are being damped so the diagram of A is like on the picture below: Now how to determine when does the A is reduced ...
0
votes
2answers
58 views

Energy of driven dampened oscillator

Given the oscillator described by: $$m\ddot{x}+\gamma \dot{x}+kx=F_0\cos(\omega t)$$ And supposing the system is at it's stable state, I wish to calculate the following: 1) The system's energy at any ...
1
vote
1answer
24 views

Is it possible to determine when an accelerometer is in a vibrating state compared to a non-vibrating state?

I would like to know if so, how raw 3-axis accelerometer data could be analyzed and manipulated real-time to register periods of vibration. The device being used has a max sample rate of 62Hz (I ...
0
votes
2answers
202 views

General Theory of Small Oscillations and existence of solutions

For small oscillations, my textbook equation for amplitude says: $(V-\omega^2T) \cdot a=0$ where $a$ is a column vector in which each component $a_i$ is related to $q_i$ as $q_i=a_i\cos(\omega ...
0
votes
1answer
31 views

Expansion in differential equation (rapid oscillating field) [closed]

Can anyone explain me how to derive the equation in (30.4)? I don't understand what approximations or substitutions are exactly performed.
0
votes
2answers
156 views

Pendulum's motion is simple harmonic motion

For a pendulum's motion to be simple harmonic motion (S.H.M.) is it necessary for a pendulum to have small amplitude or S.H.M. can be produced at large amplitudes as well? If it is really necessary ...
5
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3answers
948 views

What is a mode?

Admittedly, this seems like a very simple question. The word mode pops up in every field of physics, yet I can't remember ever having read what I felt was a precise and sensible definition. After ...
1
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1answer
79 views

Hamiltonian of coupled oscillators

Let's say I have a system of coupled oscillators which are described by the coordinates $\{x_1,...,x_N\}$ and $\{\dot{x}_1,...,\dot{x}_N\}$. The equation of motion for each oscillator is $$\ddot{x}_n ...
0
votes
2answers
43 views

Why does a block 2 on a oscillating block 1 start sliding at the maximum acceleration?

A block of mass $ m_{1} $ is oscillating horizontally with another block on it of mass $ m_{2} $. There's friction "k" between both blocks, so the thing is why the second mass starts sliding at the ...
0
votes
2answers
100 views

Calculating trajectory of particle moving in a potential (SHM)

I have been given the potential of a simple harmonic oscillator: $$V=\frac{1}{2}kx^{2}$$ I want to calculate the value $x(t)$ of a particle moving in this potential, with initial conditions ...
0
votes
1answer
44 views

Pitch and loudness relation

Using an Oscillator in a program, I noticed that the lower and the higher frequencies are less loud than the middle ones. I suspect there is a relation between pitch and loudness but can it be ...
2
votes
0answers
46 views

Simulation of oscillator with frequency dependent damping

What would be the equation for the frequency dependent damping of harmonic oscillator? Is there something like: $$ \ddot{x}+2\delta\dot{x}+\omega_0^2x = \frac{F}{m}f(t) $$ with frequency dependent ...
0
votes
2answers
66 views

What is the main key to distinguish the oscillator from the two system?

Let a circular hoops of radius $r$, is hanging on nails in a wall. Can I consider this as simple pendulum so the frequency $\omega = \sqrt{\frac{g}{L}}$? On the other hand If I consider that ...
0
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0answers
47 views

Oscillation Period — Springs

I'm trying to find an unknown mass. Both masses are attached to a spring. Mass A weighs 215 kg and the other is unknown. Both masses are oscillating in an area of no gravity and the period is equal to ...
0
votes
2answers
240 views

Current in Inductor and Capacitor with DC voltage source? [closed]

A DC source in series with pure Inductor and pure Capacitor no Resistance. How the current will flow in this circuit? What I just know is that in the beginning Inductor will behave as an open circuit ...
0
votes
1answer
117 views

Why pendulum does not follow SHM for larger angular displacement?

Considering an ideal case(neglecting drag of air, damping etc.), a pendulum follows SHM if the angular displacement is small (upto 10 degrees). But, for large angular displacement(more than 10 ...
2
votes
2answers
55 views

In Electron Spin Resonance, what provides the energy for the transition?

I recently performed an ESR experiment at M.Sc. level. The experiment manual says that the energy for the transition is provided by magnetic field oscillating at radio frequency. I am little confused ...
1
vote
1answer
37 views

How to Vary the wavelength of UV CFL? [closed]

I have a $12$ $V$ $DC$ operated UV $[CFL]$(http://en.wikipedia.org/wiki/Compact_fluorescent_lamp) with $365$ $nm$ wavelength. I need to vary this wavelength in the $250-300-350-400-450-500$ $nm$. ...
1
vote
2answers
99 views

Oscillation of Atom

What exactly does it mean when one says 'one atom of Caesium 137 oscillates 9,192,631,770 times'? I do understand the general thing about oscillation but what exactly is the oscillation of atom, what ...
-1
votes
1answer
52 views

Forced damped harmonic motion, angular frequency at which amplitude is maximum. differentiation [closed]

$$A_0 = \frac{(F_0/m)}{\sqrt{(\omega_0^2-\omega_d^2)^2+b^2\omega_d^2/m^2}}$$ How would I differentiate this with respect to the driven angular frequency (equating to zero) in order to obtain the max ...
0
votes
0answers
39 views

How long does it take for disturbed water to stop making sound?

Suppose I have a bowl with water or another liquid. The water from the bowl is perfectly quiet. Then I throw a stone in the water and I wait. How can I calculate the time after which the water is ...
5
votes
1answer
181 views

Why is the wave equation so pervasive?

The homogenous wave equation can be expressed in covariant form as $$ \Box^2 \varphi = 0 $$ where $\Box^2$ is the D'Alembert operator and $\varphi$ is some physical field. The acoustic wave ...
1
vote
1answer
118 views

What really is the significance of the resonant frequency in terms of “ease of vibration”?

I was studying the concept of resonant frequency and I've read quite a few articles and notes on it. What I have understood from what I have read is that the resonance frequency of an object is its ...
3
votes
3answers
151 views

What is the time period of an oscillator with varying spring constant?

It is well known that the time period of a harmonic oscillator when mass $m$ and spring constant $k$ are constant is $T=2\pi\sqrt{m/k}$. However, I would be interested to know what the time period ...