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31 views

Dynamics of pendulum coupled to a gyroscope [on hold]

We know the dynamics of a pendulum and we know the dynamics of a gyroscope. I put together the following I diagram below. The interesting thing as that the system has a beat frequency where the ...
6k views

Why are the harmonics of a piano tone not multiples of the base frequency?

I was trying to figure out which piano keys were being played in an audio recording using spectral analysis, and I noticed that the harmonics are not integer multiple of the base note. What is the ...
406 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?
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Vertical and Horizontal Oscillations With the same period and speeds

Why do vertical and horizontal springs with the same masses attached oscillate with the same period and the same speeds at matching positions? Assume that the horizontal surface is frictionless and ...
185 views

Interaction of a pendulum with other pendulums hanging at different heights

This is a question from a competitive test. I am not sure how to reason this out. By the length of the string, S should have the maximum amplitude. But this would be the case only when the pendulum P ...
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Electrical equivalent of inverted pendulum

Background I am working on a summer project to design labs for undergraduate students. One of the topics is feedback and there is already quite a lot of stuff about passive feedback, so we might add ...
294 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 ...
317 views

Oscillation of a Bose Einstein condensate in a harmonical trap

We were asked to try to make a theoretical description of the following phenomenon: Imagine a 2D Bose Einstein condensate in equilibrium in an harmonical trap with frequency $\omega$. Suddenly the ...
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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 ...
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Are resonance and resonant frequency the same?

Resonance is when applied oscillation is in phase with natural oscillation. Then, what is resonant frequency?
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Standing waves on compound string

Please help with this question - No data is given as such. The 2 strings have different thickness. Initially, minimum frequency of the thick string is 120 Hz. Then if we push the cart such that only ...
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Which AC bridge circuits are oscillators? [migrated]

There are different types of AC bridge circuits like the Wheatstone bridge, Maxwell, Hay, Shering and Wien. I need to know which ones are oscillators but I still don't get the main reason why the ...
57 views

Determination of nature frequency and differential equation of vibration of Hartnell governor?

I found this solution for the nature frequency but here it does not include the Ball weight and centrifugal force in the moment balance equation about the pivot (O), it is wrong answer...is not it? ...
29 views

Conditions to find standing waves harmonics

I came up with a doubt on standing waves conditions. The type of question I find difficult to answer is of the following type. Consider a rope. I do not know if the rope is fixed at both end or at ...
34 views

Oscillation of a simple pendulum [closed]

What is maximum possible time period of oscillation of a simple pendulum on earth? Please elaborate your answers.
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Is this differential equation (for damped & driven physical pendulum) physically valid?

Following is the equation of motion for a physical pendulum which is damped and driven by a force of frequency $f$: $$\frac{d^2 \theta}{dt^2} + b \frac{d\theta}{dt} + sin(\theta) = Tsin(2\pi ft)$$ ...
126 views

I am reading about the Special relativity and the original Einstein papers from 1905 and 1920 where he derives the Lorentz transformation and the effects of the time dilation and space contraction ...
60 views

Finding resonant amplitude [closed]

For a system of oscillations described by the differential equation: $$\cfrac{d^2x}{dt^2} -\epsilon \cfrac{dx}{dt} + x = \cos(\omega t)$$ We find that the response amplitude $R(\omega)$ to be: ...
173 views

Neutrino mass and energy question

If a neutrino has mass then it travels less than the speed of light. Suppose I boost myself to the rest frame; i.e. bring it to rest in the laboratory. Now if it oscillates between different states ...
18 views

Relation between Qualiy factor and FWHM

I know how to show that the Quality factor $Q=\omega/\nu$ of a damped harmonic oscillator (for example like in this link: http://farside.ph.utexas.edu/teaching/315/Waves/node11.html). What I don't ...
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Why does the period of a pendulum decrease in an accelerating frame? [duplicate]

If there is a simple pendulum in a non-accelerating frame with period $T_1$, it will have period $T_2 < T_1$ when placed in a frame accelerating perpendicularly to the direction of gravity. Why?
51 views

Pendulum and simple harmonic motion

I have a physical pendulum that, for small oscillations, can be modeled with the simple harmonic motion approach. In determining the motion equation, I need to figure out the amplitude: I know that ...
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 ...
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Independence of Period and Amplitude in Simple Harmonic Motion

In Simple Harmonic Motion, the period $T$ of an oscillation, is said to be independent of the amplitude $A$ of an oscillation, but why is that so? Attempting to derive from the equations of Simple ...
34 views

How do I draw the force field lines of an isotropic oscillator?

In general, how do I draw the force field lines (in the sense of Faraday, i.e. continuous curves whose tangents give the directions and the density of lines give the intensity of the field) of a ...
26 views

How to count such a huge number of oscillation in atomic clock? [duplicate]

A second is defined as time taken for 9,192,631,770 oscillations of caesium hyperfine levels. But it's not exactly that the electron moves up and down between these two levels. So it must be related ...
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Where is the periodic nature in the Cs atomic clock? [closed]

In case of pendulum clock,lets say one swing ticks one second..but what is the analogy in case of CAESIUM atomic clock? Is 9,192,631,770 ticks is equivalent to one tick in pendulum clock? And how we ...
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When a particle oscillates with simple harmonic motion, the period of the oscillation is [closed]

When a particle oscillates with simple harmonic motion, the period of the oscillation is... a) ...directly proportional to the displacement from the origin b) ...directly proportional to the ...
179 views

Rope waves with a twist

In the picture you see a person walking a slackline. A slackline is a tensioned flatband of polyester. Typical tensions are between 1Â kN to 15Â kN depending on the length of the line. The lines are ...
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What is the exact mathematical definition of oscillation/vibration?

My question is basically is what criteria need to be fulfilled to decide wether a motion is osciliiation/vibration or not. I found two definitions, def1: "moving around an equilibrum", def2: "...
32 views

Pendulum with Viscous and Frictional Damping

I am trying to model a pendulum with both viscous and frictional (Coulomb) damping. The problem is that the viscous damping only occurs in one direction because I am modeling a dashpot that only has ...
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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 ...
50 views

Amplitude of damped driven harmonic oscillator [closed]

I have a question that I can reason physically but mathematically I am not sure if my approach is correct. The amplitude of the oscillator is: A(\omega) = \frac{QF_{0}}{m}(\frac{1}{\omega_{0} \...
32 views

At what times is the energy in an LC oscillator completely electric or completely magnetic?

I know that the time period of the LC oscillations is given by $T=2\pi\sqrt{LC}$. At what times is the total energy of the circuit completely stored in the capacitor or completely in the inductor?