oscillations Questions

A body executes simple harmonic motion. The potential energy (P.E.), the kinetic energy (K.E.) and total energy (T.E.) are measured as function of displacement $x$. Which of the following statement is true?

The displacement of a particle varies according to the relation $x=4(\cos \pi t+\sin \pi t)$. The amplitude of the particle is:

Two particles $A$ and $B$ of equal masses are suspended from two massless springs of spring constants $k_1$ and $k_2$ respectively. If the maximum velocities during oscillations are equal, the ratio of amplitudes of $A$ and $B$ is:

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 SHM of time period $T$. If the mass is increased by $m$, the time period becomes $5T/3$. Then the ratio $m/M$ is:

The length of a simple pendulum executing simple harmonic motion is increased by $21\%$. The percentage increase in the time period of the pendulum of increased length is:

In an oscillating $LC$ circuit the maximum charge on the capacitor is $Q$. The charge on the capacitor when the energy is stored equally between the electric and magnetic field is: