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Resonance takes place when external driving frequency equals the natural frequency of an object. I know every objects have their natural frequency. But I can't see everything vibrating on its own, maybe because of damping. Is that true?

If there was a planet where every friction is neglected, can an object vibrate in its natural frequency?

For an object to vibrate in natural frequency, like a pendulum, do we have to initially apply a momentum, not periodically, just to initiate the object to vibrate?

In Bartons pendulum, if the driver pendulum starts oscillating, the same length pendulum (I will take this as B) attached to the main string will starts to resonate. So already the B pendulum should vibrate on its natural frequency, that's why when external and equal frequency given it has started resonating. But if there is a hypothetical condition where natural frequency is totally dambed in pendulum B. If the driver pendulum starts to oscillate can pendulum B resonate?

And if the external forced frequency equals the natural frequency of an object which is at rest. First it will try to oscillate in natural frequency but as the forced frequency is continuously present there, it starts resonating instead of vibrating at natural frequency. Is this true?

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  • $\begingroup$ You need to focus on a basic question with a single example of application rather than posing multiple application scenarios . If you have questions about a specific application, do that later. $\endgroup$
    – Bill N
    Jul 23 at 12:18
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There are many questions here. I'll try to give you the basics.

If you connect an inertance (mass, inductor, etc.) to a compliance (spring, capacitor, etc.) you will find that the energy associated with flow through the inertance is 180 degrees out of phase with the energy flow through the compliance. This means that if you excite this system, the energy will flow out of the inertance and into the compliance, then back into the inertance, then back into the compliance, back and forth forever (unless there is friction). This is called resonance.

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Many of your questions can be answered by considering a child on a swing.

  • You apply an initial push, a force adding momentum, to initiate the swinging.

  • The swinging then happens as a slightly damped pendulum that over time reduces its amplitude gradually - the damping is due to air resistance and possibly for old rusty swings due to friction at the hinge bearings and the like.

  • You can prevent the damping by providing continuous pushes - pulses - of momentum. You do that by pushing in phase with the natural swinging that is already ongoing. By doing that you create resonance, which is constructive interference of your influence onto the swinging which builds it up.

Had there been no damping - no air resistance or hinge friction - then you would need to push to keep up the swinging. If you still do, then the swinging increases and increases in amplitude. This is how undamped resonance looks.

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Without an external driving force a the oscillations of a damped system will decay.

A system can be excited into oscillating at its natural frequency by the application to it of an external (impulsive) force.

In general if a system has a natural frequency of oscillation, $\omega_{\rm natural}$ and is forced to oscillate by an external force which has a different frequency of oscillation, $\omega_{\rm external}$, the motion of the system will consist of two components.
An oscillation at the natural frequency of the system, $\omega_{\rm natural}$ which will decay down to zero due to the damping which the system is subjected to. This is called the transient response of the system.
An oscillation with a frequency of the external force, $\omega_{\rm external}$, which will be of constant amplitude. This is called the steady state response of the system.

After an appropriate passage of time a system will be seen to oscillate with a constant amplitude at the frequency of the external force, $\omega_{\rm external}$.

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