# Questions tagged [oscillators]

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### 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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### 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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### 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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### 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 ...
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### Understanding a reference (Cummins on 2d order ODE)

In the first page of The Impulse Response Function and Ship Motions (Cummins, 1962), it is written that: We can now write an equation, which has the appearance of a differential equation, relating ...
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### Swing - time taken [duplicate]

I was thinking about how I would go about calculating the time taken for a swing to swing from one side to the other, assuming that there only exists a gravitational force and discarding all other ...
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### How is the simple damper equation derived?

I know the spring is modeled as $F_{\text{elastic}} = k\cdot x$ when the displacements are small since this is empirically based, but what happens with $F_{\text{damping}}=c\cdot\dot{x}$? It is the ...
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### Small Angle Approximation for Simple Pendulum

I am working on a simple pendulum problem. The $y$ direction is vertical and the $x$ direction is horizontal. Displacement in the $x$ direction is taken to be much less than the length of the string, ...
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### Why is a parallel RLC circuit usually driven by a current source?

Almost always when I see an example of a parallel RLC/LC circuit diagram online, the circuit is driven by a current source instead of a voltage source. On the other hand, the series RLC is always ...
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### Implementing a spherical pendulum

I am trying to implement a spherical pendulum. The Lagrangian (which I haven't fully understood so yet) based on $l$, θ and φ taken from this page result in the equations: \begin{align} \...
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### Why do two things lose contact only when normal = 0?

Why do two things lose contact only when normal = 0? For example, I was doing a question in which a massless plank was attached to a spring. The plank also had a block of mass m kept on it. The whole ...
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### Application of linear constant coefficients ODE of the second order [closed]

I've asked this question in math forum. Apparently this question is not welcomed there. So maybe here I can get a proper response. Consider ODE in the form of $$y''+ay'+by=f(t)$$ where $a$ and $b$ are ...
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### Complex solutions to an Underdamped Oscillator

In many of the books talking about damped simple harmonic motion, the underdamped oscillator is treated as follows: Newton's second law says $$m\ddot{x} + r\dot{x} + sx = 0$$where s is stiffness ...
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### What is the difference between “monochromatic” and “impulse” force?

In a paper I am reading (linked below), the following is stated: The transient motions of the sphere and the gas bubble in the elastic, incompressible, inviscous medium are investigated in response ...
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### Damped mechanical wave

a string with density $\rho$ and tension $T$ is bound at it's two ends at $x=0$ and $x=L$. there is a force acting on the string proportional to the velocity $F(x,t)= -2\gamma \rho \dot \psi(x,t)$ ...
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### Professor and textbook disagree on frequency at which a pendulum oscillates

We had a guest lecturer today who told us that the frequency at which a pendulum oscillates is $\omega=\sqrt{mgL/I}$. However the textbook states that is $\omega=\sqrt{g/L}$. Why the discrepancy?
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### Harmonic oscillators in fluids and driven oscllations

If given a normal spring/mass system and letting the mass oscillate in a fluid say water, would it be possible for the motion of the fluid, if the fluid is moving to create a driven oscillation and ...
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### Why is the tension in a pendulum string highest when it is at the mean position?

Why does the string of a pendulum have max tension when it is at the mean position?
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### Impedance Matching in a String

I was reading 121st page of HJ Pain's Vibrations and waves and I saw this with the derivation of impedance matching on a string :- The conditions derived were: The impedance of coupling string be ...
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### What is an anisotropic harmonic oscillator?

I can't find any explanation of it anywhere in the internet. How is it different from an isotropic harmonic oscillator?
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### Forced Oscillations and Complex Representation

An oscillating force $F \cos \omega t = \Re\{Fe^{i\omega t}\}$, where $F$ is real, is applied to a mass $m$ on the end of a spring with spring constant $k$. The displacement, $x$, of the particle can ...
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### Interpreting derivatives

So we have a function such that the distance moved by a particle (say $s$) is proportional to $sin(Ct)$ where $C$ is a constant. Now i needed to show that the rate of change of velocity is directly ...
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### Significance of the complex component in the underdamped harmonic motion equation [closed]

The following differential equation represents the motion of a body of mass $m$ and displacement $x$ from the mean position, that is attached to a spring of force constant $a$ and viscous damping ...
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### Do we need a small displacement to create a oscillatory motion on the spring?

Do we need a small displacement to create a oscillatory motion on the spring with a mass attached to it? Whats the limit of the displacement that we can give initally to create a oscillatory motion? ...
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### Oscillator with decaying restoring force

Suppose a system that is described by the equation of motion: $$\ddot{x} = -k\cdot x\cdot \exp\left(-\frac{t^2}{2\sigma^2}\right).$$ (For example a spring with decaying stiffness.) I'd like to ...
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### Why does the length of a pendulum cause different natural frequencies of pendulums in Barton's pendulum?

In Barton's pendulum, the pendulum with string that is the same length, L, as the brass bob (source of driving frequency) has natural frequency equals to the bob's driving frequency. The pendulum ...
### Why is $Q$ factor an important quantity for electrical oscillations transmitting radio waves?
My textbook says that "$Q$ factor is an especially important quantity for electrical ossicilations trasnmitting radio waves. When selecting radio and television stations it is essential that the ...