Questions tagged [oscillators]

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$Q$-factor of oscillator

Given the equation for a damped oscillator is $$\ddot{x}+\gamma\dot{x}+\omega_0^2x=0$$ Is the $Q$ factor of the system given by $\omega_0/\gamma$ or $\omega_0/2\gamma$? I have seen both forms come ...
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Damped forced Oscillation with variable external frequency

Consider that we have the following forced vibration with an input frequency $ω(t)$ variable in time. $$m\ddot{x}+c\dot{x}+kx = F_0 \sin{(\omega(t) t)}$$ Assuming that the solution must be a ...
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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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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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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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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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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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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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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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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 ...