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1 vote
2 answers
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Frequency of Damped Vibrations [duplicate]

In the chapter sound, my book states that the Frequency of damped vibrations is less than the natural frequency but I could not understand this because in damped vibrations the amplitude decreases and ...
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0 votes
0 answers
2k views

What is the difference between Natural frequency and Resonant frequency? [duplicate]

I was previously under the impression that natural and resonant frequencies are the same. However, after doing some research they don't appear to be the exact same. Could someone please explain the ...
AlevelPhysicsStudent's user avatar
2 votes
1 answer
2k views

Why damping affect natural frequency of simple harmonic motion? [duplicate]

I am curious about that since damping will not affect frequency of SHM, then why it does affect on the natural frequency of the SHM. In the resonance damping graph the peak amplitude become lower but ...
Pck Tsp's user avatar
  • 83
1 vote
0 answers
185 views

Forced Vibrations [duplicate]

Forced Vibrations are the vibrations under the influence of an external periodic force. Their amplitude depends on the frequency of the external force. If it is equal to the natural frequency of the ...
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0 votes
0 answers
59 views

Forced Oscillations: What exactly is happening? [duplicate]

In a forced oscillation, what exactly is happening? My textbook says that: The oscillator, initially, oscillates with the natural frequency. When we apply external periodic force, the oscillation with ...
Kaushik's user avatar
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0 votes
0 answers
21 views

Fourier Transform of Damped Oscillations - Zero Frequency Peak and Shift [duplicate]

A damped oscillator has the time evolution: $$ y(t) = e^{-\Gamma t}\cos^2(\tilde{\omega}_0 t)$$ where $\Gamma$ is the damping rate, $\tilde{\omega}_0^2=\omega_0^2-\Gamma^2$ and $\omega_0$ is the ...
Angus's user avatar
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8 votes
7 answers
927 views

Is resonance a general property of second-order differential equations?

I have read at this site as an answer at a question about how antennas work but that is not important The resonant frequency of an antenna is determined by its constitution. Mathematically speaking, ...
Larsa se eidaklaxtarsa's user avatar
17 votes
3 answers
15k views

Definition of the $Q$ factor?

According to Wikipedia, the $Q$ factor is defined as: $$Q=2\pi\frac{\mathrm{energy \, \, stored}}{\mathrm{energy \, \,dissipated \, \, per \, \, cycle}}.$$ Here are my questions: Does the energy ...
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14 votes
2 answers
5k views

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

Consider a forced, damped harmonic oscillator $$\ddot{\phi} + 2\beta \dot{\phi} + \omega_0^2 \phi = j(t) \, .\tag{1}$$ If I pick a sinusoidal driving force $j(t) = A \cos(\Omega t)$, I find $$\phi(t) =...
DanielSank's user avatar
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6 votes
3 answers
4k views

Physical reason behind having greater amplitude when driving frequency$ < $ natural frequency than that when driving frequency $>$ natural frequency

This is quoted from A.P.French's Vibrations & Waves: If the driving force is of low frequency relative to the natural frequency, we would expect the particle to move essentially with the driving ...
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5 votes
5 answers
1k views

Why are the resonant frequencies for displacement, velocity and acceleration different in a damped oscillator?

Consider a driven harmonic oscillator under a sinusoidal force $x''(t) + \gamma x'(t)+ \omega_0^2 x(t) = F(t)$. In the regime of light damping ($\omega_0/\gamma > 0.5$), we find resonance (maximum ...
user246795's user avatar
4 votes
2 answers
9k views

Natural and Resonance frequencies of a damped oscillator

The damped oscillator equation is \begin{equation} m\ddot{x}+b\dot{x}+kx=0 \end{equation} And its solution has natural frequency $\omega_0$ \begin{equation} \omega_0=\sqrt{\frac{k}{m}-(\frac{b}{2m})...
P. C. Spaniel's user avatar
2 votes
3 answers
7k 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 ...
Rhei's user avatar
  • 131
3 votes
2 answers
3k views

Finding the resonance frequency for forced damped oscillations

I have a problem regarding a forced, damped harmonic oscillator, where I'm trying to find the resonance frequency. I have calculated the frequency for free oscillations as $$\omega_{free}=\sqrt{\frac{\...
Jonas Broe Bendtsen's user avatar
-2 votes
2 answers
6k views

Why doesn't amplitude increase when drive frequency is above resonance?

Why doesn't amplitude increase when the frequency of external periodic force increases above the natural frequency of the vibrating object?
Rakhal Chandran.B's user avatar

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