Question

A simple harmonic oscillator oscillates, with amplitude a. At what point of its motion, is the power delivered to it by the restoring force maximum( a )when it is at a displacement from the equilibrium point and moving towards the equilibrium point( b )when it is at the maximum displacement( c )when it passes through the equilibrium point, either way( d )when it is at a displacement from the equilibrium point and moving away from the equilibrium point

Answer 1

Answer:

( a )when it is at a displacement from the equilibrium point and moving towards the equilibrium point

Explanation:

As we know that restoring force on harmonic oscillator is given as

$F = -m\omega^2 x$

also we know that the velocity of the oscillator is given as

$v = \omega\sqrt{A^2 - x^2}$

now power is given as

$P = F.x$

so we have

$P = (m\omega^2x)\omega\sqrt{A^2 - x^2}$

so we have

$P = m\omega^3\sqrt{A^2x^2 - x^4}$

so we will have maximum power when

$\frac{dP}{dx} = 0$

$2A^2x - 4x^3 = 0$

$x = \frac{A}{\sqrt2}$

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Topic : SHM

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