Two pendulums with identical bobs and lengths are suspended from a common support such that in the rest position the two bobs are in contact. After being displaced by $5^o$,the bob $A$ is released from rest at $t = 0$. Subsequently,it collides elastically head-on with the other bob $B$. Identify the graph showing the variation in energy of pendulum $A$ with time for $0 \leqslant t \leqslant T$ (where $T$ is the period of either pendulum).

Column $I$ describes some situations in which a small object moves. Column $II$ describes some characteristics of these motions. Match the situation in Column $I$ with the characteristics in Column $II$.

Column $I$	Column $II$
$(A)$ The object moves on the $x$-axis under a conservative force such that its speed $v = c_1 \sqrt{c_2 - x^2}$,where $c_1, c_2 > 0$.	$(p)$ The object executes simple harmonic motion.
$(B)$ The object moves on the $x$-axis such that its velocity $v = -kx$,where $k > 0$.	$(q)$ The object does not change its direction.
$(C)$ An object is attached to a spring in an elevator accelerating upwards with constant acceleration $a$. The motion is observed from the elevator.	$(r)$ The kinetic energy of the object keeps on decreasing.
$(D)$ The object is projected vertically upwards with speed $2 \sqrt{GM_e / R_e}$.	$(s)$ The object can change its direction only once.

$A$ man weighing $60\ kg$ stands on the horizontal platform of a spring balance. The platform starts executing simple harmonic motion of amplitude $0.1\ m$ and frequency $\frac{2}{\pi}\ Hz$. Which of the following statements is correct?

The amplitude of a particle executing $SHM$ about $O$ is $10 \, cm.$ Then:

Fill in the blanks:
$1.$ If a tunnel is dug along the diameter of the Earth and a body is dropped freely in it,the motion of this body is .........,assuming there is no frictional force of the medium acting on it.
$2.$ When a body executes simple harmonic motion and makes $\frac{1}{2\pi}$ oscillations,its phase increases by ......... $rad$.
$3.$ For a body executing simple harmonic motion,the phase increases by ......... every second.
$4.$ The ratio of force constants of two springs is $1:2$ and the ratio of their mechanical energies is $2:9$. The ratio of the amplitudes of the two bodies suspended at the ends of the springs is .........

$A$ particle is executing $SHM$ with an amplitude $A$ and angular frequency $\omega$. The ratio of the maximum acceleration to the maximum velocity of the particle is: