Question 161: Oscillations

Question

Starting from the origin a body oscillates simple harmonically with a period of $$2$$ $$s.$$ After what time will its kinetic energy be $$75\% $$ of the total energy?

Accepted Answer

$$K.E.\,$$ of a body undergoing $$SHM$$ is given by,
$$K.E. = {1 \over 2}m{a^2}{\omega ^2}{\cos ^2}\,\omega t,$$
$$T.E. = {1 \over 2}m{a^2}{\omega ^2}$$
Given $$K.E.=0.75T.E.$$
$$ \Rightarrow 0.75 = {\cos ^2}\omega t \Rightarrow \omega t = {\pi  \over 6}$$
$$ \Rightarrow t = {\pi  \over {6 	imes \omega }} \Rightarrow t = {{\pi  	imes 2} \over {6 	imes 2\pi }} \Rightarrow t = {1 \over 6}s$$

Answer

$${1 \over 6}s$$

Answer

$${1 \over 4}s$$

Answer

$${1 \over 3}s$$

Answer

$${1 \over 12}s$$

Oscillations

Starting from the origin a body oscillates simple harmonically with a period of $2 s. After what time will its kinetic energy be 75\% $ of the total energy?

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