The kinetic energy and potential energy of a particle executing simple harmonic motion will be equal,when displacement (amplitude = $a$) is

When the displacement is half the amplitude,the ratio of potential energy to the total energy is

$A$ linear harmonic oscillator of force constant $2 \times 10^6\, N/m$ and amplitude $0.01\, m$ has a total mechanical energy of $160\, J$. Which of the following statements is correct?

$A$ body of mass $m$ is executing $SHM$ with amplitude $a$. When its displacement $x = 1$ unit,the force is $b$. What will be its maximum kinetic energy?

$A$ body starting at $t=0$ from the origin oscillates simple harmonically with a period of $4 \ s$. After what time will its kinetic energy be $75 \%$ of its total energy?

The kinetic energy of a particle executing simple harmonic motion in a straight line is $pv^2$ and the potential energy is $qx^2$,where $v$ is the speed at a distance $x$ from the mean position. Its time period is given by the expression: