The restoring force of a spring with a block attached to the free end of the spring is represented by

$A$ particle of mass $m$ is attached to $3$ springs $A$,$B$ and $C$ of equal force constant $K$ as shown in the figure. If the particle is pushed slightly along the line of spring $C$ and released,find the period of oscillation.

$A$ particle of mass $m$ is attached to one end of a massless spring of force constant $k$,lying on a frictionless horizontal plane. The other end of the spring is fixed. The particle starts moving horizontally from its equilibrium position at time $t=0$ with an initial velocity $u_0$. When the speed of the particle is $0.5 u_0$,it collides elastically with a rigid wall. After this collision:
$(A)$ the speed of the particle when it returns to its equilibrium position is $u_0$.
$(B)$ the time at which the particle passes through the equilibrium position for the first time is $t=\pi \sqrt{\frac{m}{k}}$.
$(C)$ the time at which the maximum compression of the spring occurs is $t =\frac{4 \pi}{3} \sqrt{\frac{m}{k}}$.
$(D)$ the time at which the particle passes through the equilibrium position for the second time is $t=\frac{5 \pi}{3} \sqrt{\frac{m}{k}}$.

All the springs in figures $(a)$, $(b)$, and $(c)$ are identical, each having a force constant $K$. $A$ mass $m$ is attached to each system. If $T_a, T_b$, and $T_c$ are the periodic times of oscillation of the three systems in figures $(a)$, $(b)$, and $(c)$ respectively, then:

$A$ mass on a spring oscillates up and down. As the mass moves downward from its highest point to its equilibrium point:

Two identical particles each of mass $m$ are interconnected by a light spring of stiffness $k$. The time period for small oscillations is equal to: