Question 136: Oscillations

Question

A particle of mass $m$ executes simple harmonic motion with amplitude a and frequency $v.$ The average kinetic energy during its motion from the position of equilibrium to the end is

Accepted Answer

KEY CONCEPT :
The instantaneous kinetic energy of a particle executing $S.H.M.$ is given by
$K = {1 \over 2}m{a^2}{\omega ^2}{\sin ^2}\omega t$
$	herefore$ average $K.E. =    =   $
$ = {1 \over 2}m\omega {}^2{a^2}  $
$ = {1 \over 2}m{\omega ^2}{a^2}\left( {{1 \over 2}} ight)$
$\left( \, ight.$ as $\left. {   = {1 \over 2}} ight)$
$ = {1 \over 4}m{\omega ^2}{a^2} = {1 \over 4}m{a^2}{\left( {2\pi v} ight)^2}$
$\left( \, ight.$ $\left. {\omega  = 2\pi v} ight)$
or,  $\,\,\,\,\,   = {\pi ^2}m{a^2}{v^2}$

Answer

$2{\pi ^2}\,m{a^2}{v^2}$

Answer

${\pi ^2}\,m{a^2}{v^2}$

Answer

${1 \over 4}\,m{a^2}{v^2}$

Answer

$4{\pi ^2}m{a^2}{v^2}$

Oscillations

A particle of mass m executes simple harmonic motion with amplitude a and frequency v. The average kinetic energy during its motion from the position of equilibrium to the end is

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