The resultant amplitude when two waves of same frequency but with amplitudes $a_1$ and $a_2$ superimpose at phase difference of $\frac{\pi }{2}$ will be,

A body of mass $5 \mathrm{kg}$ is suspended by a spring balance on an inclined plane as shown in figure. The spring balance measures,

A block of mass $m$ is resting on a piston which is moving vertically with a SHM of period $1 \mathrm{s}$. The minimum amplitude of motion at which the block and piston separate is: (Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

Acceleration $a$ versus time $t$ graph of a body in SHM is given by a curve shown below. $T$ is the time period. Then corresponding graph between kinetic energy $\mathrm{KE}$ and time $t$ is correctly represented by,

On a smooth inclined plane, a body of mass $M$ is attached between two springs. The other ends of the springs are fixed to firm supports. If each spring has force constant $K$, the period of oscillation of the body (assuming the springs as massless) is