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Questions tagged [oscillators]

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Resonance and energy flow

In this post, Alfred Centauri describes the resonance as a phenomenon which appears when 'the energy flow from the driving source is unidirectional' and then shows that this is the case for $\Omega=\...
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Damped forced vibration Calculating amplitude and phase angle

Consider that we have the following forced vibration with preload ($kxo$) spring. $$m\ddot{x}+c\dot{x}+k( x+xo) = F_0 \sin{(\omega t)}$$ Assuming that the solution must be a harmonic form but with ...
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0answers
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Spring oscillation model

When a spring - in real world - is extended $Xo$ from its natural position, it oscillates and eventually decreasing it's amplitude with time, comes to a stop. Is this a damped system or no? If yes how ...
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1answer
48 views

What is the difference between reciprocating and oscillating motion? How is reciprocating motion different from simple harmonic motion?

I wanted a good explanation for the difference between reciprocation and sinusoidal motion (For e.g. SHM). This question has been posted here due to many ambiguous and unclear explanations round the ...
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2answers
63 views

Modification of the Verlet algorithms for the pendulum problem

I'm trying to write a program to integrate the motion equations of the pendulum in the damped and forced case, that is, following this equation: $$ \frac{d^2\theta}{dt^2}=-\frac{g}{L}\sin(\theta)-\mu\...
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Frequency of the Primary Circuit in a Spark Gap Tesla Coil

In a simple spark gap tesla coil, how does the oscillating current in the primary circuit interact with the supply voltage/current? If the power supply comes from a transformer hooked up to the ac ...
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0answers
49 views

How to evaluate the period of a particle in a system with potential energy $U=-U_0/\cosh^2(\alpha x)$?

I am working through the textbook "Mechanics", from the series "Course of Theoretical Physics " by Landau and Lifshitz. In Chapter 3, where the authors talk about integrating the equation of motion $E=...
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1answer
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How can dissipative/friction terms be incorporated into a Lagrangian?

I'm trying to find a suitable Lagrangian for a damped harmonic oscillator, a system that satisfies the following equation of motion: $$m \ddot{x} + \gamma \dot{x} + \frac{d\phi}{dx} = 0.$$ What I ...
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String conservation with springs

I was trying to solve this Problem that asked to find the period of small oscillations for this system. To do so I used the fact that for a massless pulley with strings around it, the sum of the ...
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1answer
38 views

Tone production in Irish Flutes?

Since it's about a technical issue, I thought that this question would fit in here the best (as opposed to the music.stackexchange-site): I'd like to know how tone-production in an irish (wooden) ...
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1answer
24 views

Electron equations of motion for plasma

I'm reading through an Introduction to Plasma Physics by Francis F. Chen, and in the simplified derivation for plasma oscillation in 1D, the book quotes the electron equations of motion as: $$mn_e\...
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1D string reflection and transmission phase

Ok, I must be missing something very obvious here. After applying the boundary conditions, we can write: $$ A_R e^{i \delta_R} = (\frac{v_2 - v_1}{v_1 + v_2}) A_I e^{i \delta_I} $$ and $$ A_T e^{...
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1answer
87 views

Quantum Theory: Why Particles Oscillate? [closed]

I understand that as the energy of a particle increases, it oscilates more visciously. I know that there isn’t a consensus on this, but are there any theories out there that explain what causes ...
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1answer
73 views

Estimate pendulum motion

I have a simple system: a pendulum and two sensors (RADAR which will tell the distance $dx$ and $v_x$ and a Gyroscope, the gyroscope is giving me the information about $\omega$ - angular velocity) as ...
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1answer
111 views

Oscillation of Chocolate bar on soda [closed]

Why does a piece of chocolate bar oscillate in soda (i.e. floats then after a while sinks and vice versa)? What parameters does the period of oscillation rely on? Is there a specific formula that ...
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3answers
61 views

Rotational Kinetic Energy of a Pendulum

By the parallel axis theorem, a pendulum that rotates around a point $P$ and a distance $l$ from it's center, has kinetic energy $E_{kin}= \frac{\omega^2}{2}(\frac{2mR^2}{5}+ml^2)$. Where R is the ...
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Why a musical instrument's string oscillates with many frequencies? [duplicate]

I am trying to understand why when we play a note on a stringed instrument, not only it oscillates with it's fundamental frequency but also the multiples of that. For instance if you play a D on the ...
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1answer
32 views

Effect of elasticity of string on simple pendulum

In a simple pendulum system, how does the extensibility/elasticity of the string affect the time period of oscillation? Would it lead to a random or systematic error? Would the elasticity of the ...
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Springs with some finite mass

Let us consider a spring which is having some finite mass. By the help of some external agent the spring has been extended by some distance $x$. Will the restoring force produced in the spring still ...
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2answers
163 views

When you increase the tension on a string, how is the standing wave affected?

I know that wave velocity is the product of wavelength and frequency, and that velocity is proportional to string tension. Does this mean that if you increase the tension on a string, the wavelength, ...
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2answers
44 views

Does damping force depend on frame of reference?

I learn that damping force with regard to forced damped oscillations is given by F = -bv where is the velocity of the object measured from ground frame. Suppose we are in a frame which is moving with ...
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1answer
62 views

Time period of an oscillatory motion [closed]

The question: A particle of mass $m$ is executing oscillation on the $x$-axis. Its potential energy is $U(x)= K|x|^3$, where $K$ is a positive constant. If the amplitude of oscillations is $a$, ...
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2answers
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Why the time period of pendulum with infinite length is $84.6$ minutes? [closed]

In a book I was reading about SHM it stated: If the length of a simple pendulum is increased to such an extent that $\ell\to\infty$, then its time period is given by, $$T=2\pi\sqrt\frac{R}{g}\...
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1answer
47 views

Pendulum in a Boat [closed]

Suppose a pendulum is kept in a boat and it is oscillating. Now if the boat is made to oscillate in the same direction or opposite to that of the pendulum, how will these affect the amplitude of the ...
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5answers
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How can I prove that a state of equilibrium is unstable?

In the particular problem I encountered, an electric field was zero at the origin and we were meant to prove that a particle at the origin was in an unstable state of equilibrium. Is it enough to ...
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3answers
84 views

Potential energy of an oscillating pendulum

The following question always confuses me. for an oscillating pendulum why the potential energy is given by: $$V = mgL(1-\cos\theta)$$ Why not $$V = mgL\cos\theta$$ Is this a convention or there ...
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How long does it take for a wave pulse on a string to get reflected from rigid boundary?

This question arises from analysis of standing waves.The incident wave has the equation $$y=Asin(kx-\omega t)$$The reflected wave has the equation$$y=Asin(kx+\omega t +\pi)$$When determining the ...
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3answers
52 views

Inserting an arbitrary phase in the equation for driven damped oscillations

In Classical Mechanics by Taylor, we find the solution to the differential equation of a damped oscillator with a sinusoidal driving force: $$\ddot{x} + 2\beta\dot{x} + \omega_0^2x = f_0\cos\left(\...
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1answer
56 views

Is energy conserved in a Van der Pol oscillator?

The Van der Pol Oscillator is governed by a 2nd order ODE with nonlinear damping. The 'position' of the oscillator is the solution to $$x''(t) = \mu (1 - x^2(t)) x'(t) - x(t)$$ Here $\mu$ controls ...
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1answer
36 views

What does the viscous damping coefficient depend on?

I’m doing a theoretical calculation involving the damping on an oscillating string, and I found the following relationship, where a certain damping factor $b$ is proportional to $\frac{c}{d^2}$ where $...
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0answers
50 views

Prove from first principles that a guitar string will vibrate at a constant frequency

From experience I am aware that a taught string will generally vibrate with a constant frequency. I wanted to prove this by considering the relation of distance from the resting position, and its ...
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1answer
72 views

What is complex frequency? [closed]

I am learning EE, and about complex frequencies, but what is its physical meaning? What is it used for? Why is it? And only happen in the laplace transform?
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1answer
157 views

Difference between simple harmonic motion and angular SHM

I am not able to decipher when it is simple harmonic motion and when it is angular harmonic motion. Can we use both of them interchangeably? Can I know all the variable analogous for angular SHM (by ...
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1answer
31 views

Oscillations - Mass Change on Simple Pendulum

The problem that I am thinking of is phrased as follows: A person on a swing is holding a sandbag and is moving with some initial velocity $v_0$ at the bottom of the swing of length $l$. The ...
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4answers
85 views

Solutions to Newton's laws with unbounded kinetic energy for inverted harmonic oscillator potential

In a one dimensional setting, Hooke's Law, together with Newton's 2nd law, results in a differential equation of the form (setting the constants $m$ and $k$ equal to 1 for notational simplicity) $x''(...
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1answer
39 views

Could the flex in a skyscraper due to wind be used to produce power?

While browsing 'Hot Questions' on Stack Exchange I came across this question: Can we use the stored gravitational potential energy of a building to produce power? It got me thinking about the use of ...
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2answers
28 views

Materials used for damping

What type of material should be used for damping? Like my course says ductile materials but then if the damper is deformed it wont be able to be used again, so how does that work? Like why not stiff ...
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2answers
57 views

Energy transfer through damping

When a damper is attached to a bridge, its tuned to the bridges natural frequency. I dont get how will that allow for maximum transfer of energy? And also how will heavily damped systems prevent ...
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1answer
168 views

Applying Kramers-Kronig relation to a simple damped oscillator

I just discovered the Kramers-Kronig relation and am trying to apply it to a simple damped oscillator of the form subjected to an impulse at $t=0$, which is a causal system: $$m\ddot x + c\dot x + k ...
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1answer
112 views

How to obtain the quantization of a simple pendulum using Bohr-Wilson-Sommerfeld rule? [closed]

How to obtain the quantization of a simple pendulum using Bohr-Wilson-Sommerfeld rule?
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1answer
27 views

Small amplitudes and Stokes drag law

Why is it that on a damped harmonic oscillator or a pendulum in a fluid, the Stokes drag law in the fluid only applied to small amplitude oscillation compared to large amplitudes oscillations? Dose ...
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1answer
70 views

To consider or not to consider potential energy of a mass attached to a spring in oscillation? [closed]

For the above system I have the following expressions for kinetic and potential energy: $$ V = \frac{1}{2}\,k\,x^{2}+m\,g\,l\,(1-cos\,\theta)-m\,g\,x\\ T = \frac{1}{2}\,m\,\dot{x}^{2}+\frac{1}{2}\,m\,...
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1answer
21 views

Damped oscilliations on a ball rolling in a U-shape

How do you calculate the rate of loss of energy on a ball moving in a U-shape (half sphere)? Can I simply look at the height of the ball at its peaks and measure the difference between the potential ...
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2answers
42 views

Restoring forces and oscillating systems

My book states, 'Restoring forces give the system it's potential energy.' And it also states, 'Inertia due to mass in mechanical system gives the system it's kinetic energy.' I don't get what is all ...
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2answers
105 views

Why $y=A\sin(kx-\omega t)$ is used in deriving standing wave equation? [closed]

In my text book equation of travelling wave is given as $y=A\sin(\omega t-kx)$ and they deduced standing wave equation using the same wave equation and arrived at $Y=2A\cos(kx)\sin(\omega t)$ but ...
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1answer
135 views

Why is frequency equal to the inverse of period?

I am really struggling with this concept, please help. I know that the period is simply the time for 1 for one complete cycle, but how come the frequency is 1 over this? It is confusing to me
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1answer
50 views

Finding the Amplitude of a Spring Oscillation given initial Position and Velocity

I'm trying to create a physics simulation, and I need to be able to determine the amplitude of the oscillation of a mass-and-spring system given any position that the mass might be in and the velocity ...
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1answer
39 views

Oscillations and Spring balances problem

Problem Statement: A spring balance has a scale that reads from 0 to 50 kg. The length of the scale is 20 cm. A body suspended from this balance, when displaced and released oscillates with a ...
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2answers
37 views

Damped drive oscillating systems

I am currently looking at the theory of find the viscosity of and object through damped harmonic motion, and tho it can be done there is obviously a limitation with regrades to the medium. If the ...
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1answer
266 views

How to derive a formula for the period of a simple pendulum? [duplicate]

The following formula is given in our lab manual: $$ T = 2 \pi \sqrt{\frac{L}{g}} \left( 1 + \frac{1}{4}\sin^2 \frac{\theta}{2} + \frac{9}{64}\sin^4 \frac{\theta}{2}+\cdots \right) $$ for the period ...