The total mechanical energy of a particle executing simple harmonic motion is $E$. When the displacement is half the amplitude,its kinetic energy will be

For a simple pendulum,a graph is plotted between its kinetic energy $(KE)$ and potential energy $(PE)$ against its displacement $d$. Which one of the following represents these correctly? (graphs are schematic and not drawn to scale)

$A$ particle is vibrating in a simple harmonic motion with an amplitude of $4\, cm$. At what displacement from the equilibrium position is its energy half potential and half kinetic?

$A$ particle of mass $m$ is executing simple harmonic motion about its mean position. If $A$ is the amplitude and $T$ is the period of $S$.$H$.$M$.,then the total energy of the particle is

As a body performs $S.H.M.$,its potential energy $U$ varies with time $t$ as indicated in:

$A$ block is in simple harmonic motion $(S.H.M)$ at the end of a spring with position given by $x = 5 \cos \left(\omega t + \frac{\pi}{4}\right)$. If the total mechanical energy is $100 \ J$,then the potential energy at time $t = 0$ is: (in $J$)