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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 $250-300-350-400-450-500$ $nm$. ...
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2answers
194 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
89 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
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0answers
45 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
216 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
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1answer
222 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
198 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 ...
0
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0answers
56 views

Period for small oscillations is like simple harmonic motion

In Arnold's book on mechanics there is the following problem: Consider the period of oscillations near a minimum $E_0$ of the potential energy function $U$. Then he says to compute the limit of ...
0
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0answers
56 views

Separation of time scales to solve ODEs

I am reading several papers that obtain approximate solutions to nonlinear ODEs using a "standard technique" to separate the time scales of the dynamics. For examples, consider the ODE (a particle in ...
0
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2answers
124 views

Why is a sine wave considered the fundamental building block of any signal? Why not some other function? [closed]

It is mathematically possible to express a given signal as a sum of functions other than sines and cosines. With that in mind, why does signal processing always revolve around breaking down the signal ...
2
votes
2answers
220 views

Showing that a mass moves a half cycle

Consider a mass $m$ at position $x(t)$ on a rough horizontal table attached to the origin by a spring with constant $k$ (restoring force $-kx$) and with a dry friction force $f$ $$\begin{cases} f=F,...
0
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1answer
367 views

Fundamental frequency of a material and its Young's modulus

I wonder if there is a connection between fundamental frequency and Young's modulus of a material. For example, how to calculate the Young's modulus of a glass bar by knowing its frequency spectrum?
2
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2answers
39 views

What determines the point of energy spillover to higher modes of a standing wave resonator?

One of the better known physics demonstrations for standing wave resonance is the singing rod . By holding the rod exactly in the middle the demonstrator constrains the first mode of excitation - the ...
0
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0answers
117 views

Kater's pendulum graph

I was told that the graph of position vs period must be a straight line in Kater's pendulum, but my findings are more curved, also after searching in google graphs are like parabolas, my question is ...
8
votes
2answers
383 views

Are there any fully analytically solvable nonlinear oscillators?

I'm trying to find a simple one-dimensional problem, in which a particle would oscillate with some energy, and the period of oscillation would depend on particle energy (unlike in harmonic oscillator)....
0
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0answers
10 views

Atoms - deflection from the equilibrium state - oscillation [duplicate]

A homogeneous, spherical electron cloud describes an atom (radius $a_0$ and total charge $^−e $ and positive point charge$^+e$ as the nucleus. An external electric field stimulates the electron cloud ...
2
votes
1answer
87 views

Analytical mechanics with SR

Is there an analytical mechanics with SR? Of course you can write down the Lagrangian and Hamiltonian of a free particle. What about non-free? Are there any problems? To be specific: what would the ...
0
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2answers
148 views

Equation for vibrating cantilever in SHM

what is the equation connecting the period of oscillation of a ruler/cantilever with its length? my relation indicates that $T\propto L^2$ but i dont know if it is good
1
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1answer
71 views

Undamped Resonance of a Classical Harmonic Oscillator

Consider an undamped harmonic oscillator. It may be driven at it's natural frequency, $\omega_0^2 = \frac{k}{m}$. According to Feynman, and other sources, were this to happen, the amplitude of the ...
1
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2answers
316 views

What is the qualitative cause for a driven oscillator to have a max. amplitude during resonance?

The steady-state motion of a driven oscillator is given by;$$x =\underset{\text{amplitude}} {\dfrac{F_0}{m({\omega_0}^2 - {\omega}^2)}} \cos\omega t.$$ As we see, the amplitude becomes maximum when $$\...
1
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1answer
204 views

General solution of a mass spring system

This is the differential equation that describes small amplitude vertical oscillations of a mass $m$ that is hanging from a spring $$\frac{d^2x}{d t^{2}} + \frac{b}{m}\frac{dx}{dt} + \frac{k}{m} x = 0$...
0
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3answers
100 views

Why is $x=C\cos(\omega t)$ the solution of $m\frac{d^2 x}{dt^2}+kx=F_o\cos(\omega t)$ though lacking two arbitrary constants?

I was studying undamped oscillator with harmonic driving force at the steady-state condition. It can be expressed in the form of differential equation as:$$m\dfrac{d^2 x}{dt^2}+kx=F_o\cos(\omega t).$$ ...
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0answers
142 views

What is the mechanism of subharmonic oscillations?

It's clear to me from linear systems theory that energy manifested within a fundamental mode of resonance can saturate with the excess energy spilling over into harmonic frequencies greater than the ...
1
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2answers
84 views

Resonance peak broadening due to losses: physical reason

I wonder why when losses are present in a oscillator, the width of the resonance peak is broadened. More precisely: why, when losses are present, can the amplitude reach nearly the maximal one (the ...
0
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2answers
131 views

In general terms, what key elements are necessary for resonance to exist in a physical system?

I found a related question An Analogy for Resonance, and John Rennie gives a good explanation using description of the harmonic oscillator. But I'm really looking for an accurate and complete list of ...
3
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2answers
77 views

Polarisation by Reflection - oscillation direction

I'm currently studying polarisation by reflection, and have come across two pieces of information from the same source, which I can't seem to understand on how they differ. The oscillation direction ...
0
votes
1answer
64 views

Definition of mechanical impedance

Mechanical impedance is in the simplest (yet common) case defined as: $$ Z_m = \frac{F}{v} $$ where $F$ is force (let's assume 1D case) and $v$ velocity of the object (let's assume point of mass). ...
1
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2answers
134 views

How to calculate the period of the movement from a potential?

I have an assignment, where I have an object moving in 1-D with a given mass and energy, and the potential V(x), and I'm supposed to calculate the period of the movement as a function of the energy $...
2
votes
1answer
135 views

Calculating pendulum rate variation due to change in force of gravity over arc of swing

Hi all and thank you in advance for any insight into this problem. I'm a journalist working on a story on precision pendulum clocks and specifically on the isochronism of pendulums. I note that the ...
0
votes
1answer
169 views

Energy dissipation in damped oscillator (not driven by any external force)

If I have a damped oscillator (with no driving force), the energy of the oscillator will decrease like: $$E(t)=E_0e^{-\gamma t},$$ where $E_0$ is some initial energy and $\gamma\in\mathbb R^ +$. We ...
2
votes
1answer
68 views

Analysis of motion of a body moving on a string?

I was wondering about something I observed yesterday. To give some background, one of my hobbies is slacklining. This is essentially like tight-rope walking but with a one inch piece of (in this case ...
1
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1answer
85 views

Quantum Harmonic Oscillators

I'm having trouble with quantum harmonic oscillators and I'm not sure how to approach these questions: . I'd really like to get my head around these concepts but I'm struggling to understand fully. ...
3
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1answer
74 views

Why is energy in a system typically able to be described using quadratic expressions?

This might be more of an applied math question. Why is the energy of a system typically able to be described using quadratic expressions. Is there an underlying mechanic that drives this?
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2answers
687 views

Period of a simple pendulum accounting for friction

The period of a simple pendulum is $$T=2\pi\sqrt{\ell/g},$$ but no where in there do I see that it accounts for friction. Does it somehow account for friction, and if not, how could you do that?
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2answers
606 views

Is the usually taught solution to forced harmonic motion just a special solution?

Let's say we have a mass on a spring being driven by a forcing function. Given hook's law, $F = -kx$, and a forcing function of $$F(t) = F_0\sin(\omega t) .$$ We can write: $$ m\frac{d^2x}{dt^2} = -...
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0answers
112 views

discrepancy in theoretical and natural frequency?

In an experiment to determine the natural frequency of a spring-mass-pulley system, why would the experimental natural frequency (found using 1/time) be greater than the theoretical natural frequency ...
0
votes
1answer
43 views

Can the logarithmic decrement be found from extension of spring?

Consider a spring-mass system in which a mass hangs freely from a spring fixed to a ceiling. Can the logarithmic decrement be found simply from the extension of the spring? The only parameters known ...
0
votes
2answers
1k views

Is an oscillation the same as a period?

Is one oscillation from peak to trough to peak again or is it just peak to trough? Doing a homework question and want to be sure I have the right definition
0
votes
1answer
67 views

Building a Crystal Radio Questions

I have been reading several books and articles about building a crystal radio and the explanations about the inner workings of the circuit seem vague. All articles and books mention the coil and the ...
0
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0answers
24 views

Frequency resonance of Bones, and other parts of the human body [duplicate]

Today in class we were learning about states of matter. I found out that in a solid the atoms are vibrating. This caused me to think about how crystal glass will break if an opera singer sings high ...
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0answers
88 views

Period of Paper Motion

A threatening note written on 8.5x11 inch paper is pinned to the door of a physics professor. The perpetrator left in a hurry so that when the physics professor finds the paper it is still swinging. ...
4
votes
2answers
831 views

Reflected and refracted light have same frequency as that of the incident light frequency. Why?

My text book says- When a monochromatic light is incident on a surface separating two media, the refracted and reflected light both have the same frequency as the incident frequency. Can anyone ...
1
vote
2answers
167 views

Calculate damping constant / coefficient

I am trying to graphically simulate a series of springs in 2D. Now one of the forces I am stuck with calculating is the damping force. The given formula is $F = -k_d v$. I know that $v$ is the ...
1
vote
3answers
1k views

Definition of a normal mode?

What is the formal definition of a normal mode for a string? And how does this relate to the definition from e.g. wiki that seem to be applied to discrete systmes of particles only? Also on a string ...
3
votes
1answer
527 views

The universality of the Stuart-Landau equation to describe nonlinear oscillators

I have read numerous papers which boldly suggest that the Stuart-Landau equation can be successfully used to model any weakly nonlinear oscillating system near a Hopf bifurcation. Even thought it has ...
1
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0answers
36 views

Data Collection of oscillatory motion

I'd like to study nonlinear oscillatory motion this semester. I plan to build several different mechanical systems (pendula, masses on springs, etc with and without driving forces, large/ small drag, ...
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0answers
20 views

Coupled Oscillation With Four Springs and Three Masses [duplicate]

"Four identical springs and three identical masses lie between two walls. Find the normal modes" The situation looks something like this:$$|---m_1---m_2---m_3---|$$ To start this problem off, I looked ...
5
votes
4answers
227 views

What is a full cycle in damped oscillation?

Maybe it seems a dumb question, but I can't understand what the cycle in a damped oscillation is? Let's take an example: In harmonic motion, one cycle is the smallest distinguishable part of wave ...
0
votes
1answer
82 views

What does multi-periodicity mean in stellar pulsations?

How can there exist multi-periodicity in stellar pulsations? http://www.kitp.ucsb.edu/sites/default/files/kitp/preprints/moskalik2.pdf How can one visualize a multi-periodic pulsation or oscillation?
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2answers
205 views

Oscillations Near Equilibrium (With Linear Differential Equations)

Case I: The force acting on an object of mass m is $F(x) = F_o(1-e^{\alpha x})$ Case II: The force acting on an object of mass m is $F(x) = F_o(1-e^{-\alpha x})$ where $F_o$ and $\alpha$ are ...