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1
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0answers
125 views

Why do trees sway?

Resonance can also occur in three dimensions (such as wind induced swaying) I tried to make a free body diagram (I know it is terribly wrong) to find the forces that causes the tree to undergo ...
6
votes
2answers
320 views

How much upward force due to ground vibrations does the Earth exert on you?

Say you're walking by the highway and you can feel the vibrations of cars moving along. How would you approximate the force that the ground is exerting on your feet due to these vibrations?
0
votes
2answers
44 views

SHM with acceleration at mean position

Suppose we have an equation of motion as $$\frac{d^2x}{dt^2} = -kx + c,$$ then can it be called a SHM? Since acceleration is still proportional to displacement. But then, how will we define the mean ...
0
votes
1answer
42 views

phase difference of two reflected wave

Suppose a tuning fork generates sound waves with a frequency of 100 Hz. The waves travel in opposite directions along a hallway, are reflected by end walls, and return. The hallway is 47.0 m long and ...
3
votes
1answer
48 views

Free body diagram when forces are not directly in contact with the object

I was trying to use Newton's second law to describe the motion of the following pendulum: However, I was confused as to how to include the spring in Newton's second law. I was able to set up a ...
0
votes
2answers
49 views

Damped sinusoidal motion with initial velocity or acceleration [closed]

I am looking for the equation of damped sinusoidal motion with an initial velocity. For example: a mass is moving by spring1 force. At ...
0
votes
2answers
67 views

Damped Pendulum (generalised)

I know the differential equation for the swinging of a simple pendulum: $\displaystyle\frac{\partial^2\theta}{\partial t^2} + \left(\frac{g}{L}\right)\sin\theta = 0$ where: $L$ is the length of ...
1
vote
2answers
207 views

Eigenvalue physical meaning [closed]

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
43 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
26 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
votes
1answer
50 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 = \frac{...
0
votes
1answer
37 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: $$ \lambda_{...
6
votes
5answers
178 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
133 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
50 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
votes
0answers
18 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
58 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
vote
1answer
47 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
vote
2answers
90 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
187 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
18 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
29 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
votes
1answer
48 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
votes
1answer
88 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
votes
2answers
103 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
44 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
vote
3answers
173 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
181 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
votes
1answer
84 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
vote
0answers
30 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
112 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
3answers
266 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
25 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
59 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
28 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
238 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 t-\...
0
votes
1answer
35 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
3answers
614 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
votes
3answers
2k 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
vote
1answer
145 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
57 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
143 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 $x(t=0)=...
0
votes
1answer
47 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
53 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
70 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
votes
0answers
64 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
460 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
243 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 degree),...
2
votes
2answers
77 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
39 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 $250-300-350-400-450-500$ $nm$. ...