MCQ
The total energy of the body executing $S.H.M.$ is $E$. Then the kinetic energy when the displacement is half of the amplitude, is
  • A
    $\frac{E}{2}$
  • B
    $\frac{E}{4}$
  • $\frac{{3E}}{4}$
  • D
    $\frac{{\sqrt 3 }}{4}E$

Answer

Correct option: C.
$\frac{{3E}}{4}$
c
(c) Total energy in $SHM $ $E = \frac{1}{2}m{\omega ^2}{a^2}$; (where $a =$ amplitude) 

Potential energy $U = \frac{1}{2}m{\omega ^2}({a^2} - {y^2}) $

$= E - \frac{1}{2}m{\omega ^2}{y^2}$ 

When $y = \frac{a}{2}$

$⇒$ $U = E - \frac{1}{2}m{\omega ^2}\left( {\frac{{{a^2}}}{4}} \right)$

$= E - \frac{E}{4} = \frac{{3E}}{4}$

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