For a particle executing S.H.M., its potential energy is 8 times its kinetic energy at a certain displacement '$x$' from the mean position. If '$A$' is the amplitude of S.H.M., the value of '$x$' is

A particle executing simple harmonic motion starts from mean position with amplitude '$A$' and periodic time '$T$'. At what displacement is its speed one-fourth of the maximum speed?

A mass $m_1$ performs S.H.M. with amplitude A which is connected to horizontal spring. While mass $m_1$ passing through mean position, another mass $m_2$ ($m_2 < m_1$) is placed on it so that both masses move together with amplitude $A_1$. The ratio of $A/A_1$ is

The maximum potential energy of a block executing S.H.M. is E and amplitude of oscillation is 'A'. The kinetic energy of the block at amplitude A/2 is