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If a body is in vacuum and clamped at one point when disturbed slightly from its rest position , starts vibrating. It vibrates in its natural frequency and constant amplitude.

So if we are disturbing the body slightly and the natural frequency of the body is its say 5Hz then the body will start vibrating at 5Hz. So where does the body get the energy to vibrate at 5Hz , because since we are not doing much work in disturbing the body the energy given to the body by us is not much right?, it is enough to make it vibrate in its natural frequency? Where does the body gets energy to vibrate in its natural frequency?

I am in 10th standard so it would be helpful if anyone answers the question based on it.

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    $\begingroup$ Did you ever notice that a bell hanging in a carillon doesn't ring until it's struck? $\endgroup$
    – The Photon
    Jul 25 at 15:53
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    $\begingroup$ "Not much work" is not the same as "no work". When you pluck a guitar string for example, you have to apply a force to move the string sideways, and that force does work. $\endgroup$
    – alephzero
    Jul 25 at 15:58
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When the body is disturbed from it's equilibrium position it is stretched or compressed slightly. There is then stored potential energy within it, this energy, when released, becomes kinetic energy.

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The energy for the vibration comes from the disturbance. If there is only a slight disturbance then there will be only a slight vibration. Since the vibration of interest is a natural resonance vibration, it does not require much energy to produce such a vibration.

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Note that the energy of the vibrating body is related to its amplitude. For a simple harmonic oscillator, you get that its energy is $$E=\frac{1}{2}m\omega^2A^2$$ where $\omega=\sqrt{k/m}$ is its frequency, $m$ is the mass, $k$ the spring constant, and $A$ the amplitude. If you perturb the body with a displacement $A$, then you are giving it an energy related to that work you made. For a large displacement, you get a system with a lot of energy and for a tiny displacement you get a small quantity of energy.

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