The average velocity of a particle performing S.H.M. in one complete vibration is ( $\mathrm{A}=$ amplitude of S.H.M., $\omega=$ angular velocity)

A mass ' $M$ ' is suspended from a spring of negligible mass. The spring is pulled a little and then released so that the mass executes S.H.M. of periodic time ' $T$ '. If the mass is increased by ' $m$ ', the time period becomes $4 T / 3$, then the ratio of $\frac{\mathrm{M}}{\mathrm{m}}$ is

A particle starts from mean position and performs S.H.M. with period 6 second. At what time its kinetic energy is $50 \%$ of total energy?

$$ \left(\cos 45^{\circ}=\frac{1}{\sqrt{2}}\right) $$

A particle of mass ' m ' is executing S.H.M. about the origin on $x$-axis with frequency $\sqrt{\frac{\mathrm{ka}}{\pi \mathrm{m}}}$, where ' $k$ ' is a constant and ' $a$ ' is the amplitude of S.H.M. If ' x ' is a displacement of a particle, at time ' $t$ ', potential energy of the particle will be