The tag has no usage guidance.

learn more… | top users | synonyms (2)

1
vote
2answers
290 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
vote
1answer
193 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
votes
3answers
98 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:$$m\dfrac{d^2 x}{dt^2}+kx=F_o\cos(\omega t).$$ ...
1
vote
0answers
129 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
vote
2answers
79 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
votes
2answers
108 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
votes
1answer
66 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
63 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
vote
2answers
122 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
125 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
160 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
66 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 ...
0
votes
0answers
31 views

Ratio of oscillation amplitudes of a box on a gasket to floor

So the problem is that I have a box and I put it on a gasket to preserve it from vertical oscillations. The gasket is compressed by the box by a quantity of $h$. The floor is oscillating at frequency ...
1
vote
1answer
83 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
votes
1answer
72 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?
1
vote
2answers
612 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?
6
votes
2answers
601 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} = ...
0
votes
0answers
106 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
41 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
879 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
63 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
votes
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 ...
1
vote
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
786 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
159 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
969 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
473 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
vote
0answers
35 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, ...
0
votes
0answers
19 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
205 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
74 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?
1
vote
2answers
204 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 ...
0
votes
1answer
65 views

If a place a spring in a box and drop the box, what happens?

Suppose I a holding a box in my hands, and inside the box a spring with some mass attached hangs from the cieling of the box. Initial the system is at equilibrium, then I let go of the box and it ...
1
vote
1answer
223 views

How to draw waves in X and Y position like this oscilloscope example?

I would like to know how to "draw sound" so i could achieve shapes like the ones in this video: http://www.modularsynth.ru/en/2014/01/24/ed120_chaotica/ I have programming background ( as in: i ...
2
votes
1answer
442 views

Forced Oscillations & Resonance

I need a very much physical explanation for the phenomenon of Resonance associated with forced oscillations (damped). I have gone through HRW and Concepts of Physics by H C Verma, but that wasn't of ...
0
votes
1answer
262 views

Difference between harmonic oscillator & coupled oscillators

Coupling, according to wiki, is the condition of two systems when they interact with each other. Now, I came across the terms harmonic oscillator and coupled oscillators. Now,what is the difference ...
1
vote
1answer
4k views

Does damping force affect period of oscillation?

In my physics notes, it has been given that the damping force increases the period of oscillation. I am unable to understand this part. How is this possible? The only relation I know is that as the ...
1
vote
1answer
466 views

Why does $k/m=\omega^2$ for harmonic motion? [closed]

Can anyone please give me a proof for $k/m=w^2$ in simple harmonic motion? I have tried energy conservation and Newton's laws as follows : In the case of a mass-spring system, $$F=ma =-kx\\ F=ma = ...
0
votes
1answer
55 views

How do I prove that frequencies that are irrationally related lead to quasi-periodic motion?

Consider the equation: \begin{equation} \dot{x} = Mx, \end{equation} where \begin{equation} M = \begin{pmatrix} i\omega_1 & 0 & \cdots & 0 \\ 0 & i\omega_2 & \cdots & 0 \\ ...
0
votes
0answers
143 views

For a bob on a pendulum following simple harmonic motion, what causes the bob to accelerate towards the centre of equilibrium?

*The position of equilibrium being the position of the bob when the string is taut and vertically downwards. When I draw a simple diagram, I see that the tension of the string, which always acts ...
1
vote
0answers
773 views

Walter Lewin's physics lecture 8.03 Waves and Oscillation [closed]

Does any of you have the files (lecture notes, assignments, exams) of Walter Lewin's course on Waves and Oscillations? I used to learn from them and it helped so much. Thanks before
2
votes
1answer
247 views

How does resonance store vibrational energy?

In the wiki article, it is written that in resonance, maximum amplitude is possible as vibrational energy is stored. What does that statement mean? How is energy stored so that max. amplitude ...
0
votes
2answers
139 views

Coupled oscillators and Normal Modes

Consider we have a system consisting of 2 arbitrary masses and 3 arbitrary springs connecting them horizontally and between fixed walls, and we want to obtain the motion of each mass after we input ...
5
votes
1answer
647 views

How do you define the resonance frequency of a forced damped oscillator?

Consider a forced, damped harmonic oscillator $$\ddot{\phi} + 2\beta \dot{\phi} + \omega_0^2 \phi = j(t) \, .$$ If I pick a sinusoidal driving force $j(t) = A \cos(\Omega t)$, I find $$\phi(t) = ...
0
votes
0answers
46 views

Small Oscillations

When a problem asks to consider small oscillations about equilibrium, I know this implies that powers higher than one can be sent to zero, but does this say anything about the velocities? For example, ...
0
votes
1answer
108 views

Why can't a pendulum vibrate in a an orbiting satellite?

People say because the pendulum would not feel any gravity, so the time period becomes infinite. However, I think the pendulum would be in a state of free fall, it would certainly feel gravity, what ...
0
votes
1answer
123 views

Can a Chaotic Pendulum be made Continuous?

Can a Chaotic Pendulum be made continuous? I mean, Is there any Method or any Arrangement for a chaotic pendulum to Oscillate forever? (never stop its motion)
0
votes
2answers
119 views

Damped Oscillations: Incoherence between a general solution and a specific one

In my 'Classical Dynamics of Particles and Systems, THORNTON/MARION, 5th Edition' book of classical mechanics it is given the following general solution for a damped oscillation solving ...
0
votes
2answers
193 views

Correlation between equations of elliptical orbits and pendulums

The equation for the period of a pendulum is: $$T=2π\sqrt{\frac{L}{g}}$$ Where 'g' is the acceleration due to the gravitational field and 'L' is the length. The equation for the period in of a body ...
-3
votes
1answer
943 views

What could be the applications of Damped Oscillation? [closed]

I've been researching on Damped Oscillation for a few days for a research paper, however I couldn't find any of its applications on the web, though there are few examples of it, but they couldn't be ...