Question

A particle performs S.H.M of amplitude 'a'. What fraction of total energy is kinetic when the displacement is half of the amplitude?​

Answer 1

when SHO completes half of the displacement it will have 50% of kinetic nd 50% of potential energy

Answer 2

The fraction of total energy and kinetic energy is  $\dfrac{3}{4}$.

Explanation:

Given that,

Amplitude = a

Displacement $y=\dfrac{a}{2}$

The total energy of the particle executing S.H.M

$E=\dfrac{1}{2}m\omega^2 a^2$

We need to calculate the kinetic energy

Using formula of kinetic energy

$K.E=\dfrac{1}{2}m\omega^{2}(a^2-y^2)$

When the displacement is half of the amplitude

$K.E=\dfrac{1}{2}m\omega^{2}(a^2-(\dfrac{a}{2})^2)$

$K.E=\dfrac{1}{2}m\omega^{2}(\dfrac{3}{4}a^2)$

$K.E=\dfrac{3}{4}E$

We need to calculate the fraction of total energy and kinetic energy

$\dfrac{K.E}{E}=\dfrac{3}{4}$

Hence, The fraction of total energy and kinetic energy is  $\dfrac{3}{4}$.

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Topic : Energy

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