The displacement-time graph of a particle executing $SHM$ is shown. Which of the following statements is wrong?

Column $I$ gives a list of possible sets of parameters measured in some experiments. The variations of the parameters in the form of graphs are shown in Column $II$. Match the set of parameters given in Column $I$ with the graph given in Column $II$.

Column $I$	Column $II$
$(A)$ Potential energy of a simple pendulum ($y$-axis) as a function of displacement ($x$-axis)	$(p)$ Parabolic curve opening upwards
$(B)$ Displacement ($y$-axis) as a function of time ($x$-axis) for a one-dimensional motion at zero or constant acceleration	$(q)$ Linear graph passing through origin
$(C)$ Range of a projectile ($y$-axis) as a function of its velocity ($x$-axis) when projected at a fixed angle	$(r)$ Linear graph with non-zero intercept
$(D)$ The square of the time period ($y$-axis) of a simple pendulum as a function of its length ($x$-axis)	$(s)$ Parabolic curve opening upwards (starting from origin)

State whether the following statements are True or False:
$1.$ If a spring is cut into two equal pieces,the spring constant of each piece decreases.
$2.$ As the displacement of a Simple Harmonic Oscillator $(SHO)$ increases,its acceleration decreases.
$3.$ $A$ system can oscillate with more than one natural frequency.
$4.$ The periodic time of Simple Harmonic Motion $(SHM)$ depends on amplitude,energy,or phase constant.

$A$ small block is connected to one end of a massless spring of un-stretched length $4.9 \ m$. The other end of the spring is fixed at $O$. The system lies on a horizontal frictionless surface. The block is stretched by $0.2 \ m$ and released from rest at $t = 0$. It then executes simple harmonic motion with angular frequency $\omega = \frac{\pi}{3} \ rad/s$. Simultaneously at $t = 0$,a small pebble is projected with speed $v$ from point $P$ at an angle of $45^{\circ}$ as shown in the figure. Point $P$ is at a horizontal distance of $10 \ m$ from $O$. If the pebble hits the block at $t = 1 \ s$,the value of $v$ is (take $g = 10 \ m/s^2$):

$A$ block of mass $(10 \alpha) \text{ g}$,where $\alpha$ is a constant,is moving with velocity $3 \text{ m/s}$ to the right. It collides inelastically with a block on the right of mass $10 \text{ g}$ and sticks to it. The right block is connected to three springs as shown in the figure. The spring constant of each spring is $k = 2 \text{ N/m}$. If the amplitude of the resulting simple harmonic motion is $A = \frac{1}{2\sqrt{2}} \text{ m}$,then the value of $\alpha$ is:

The center of a disk of radius $r$ and mass $m$ is attached to a spring of spring constant $k$,inside a ring of radius $R > r$ as shown in the figure. The other end of the spring is attached on the periphery of the ring. Both the ring and the disk are in the same vertical plane. The disk can only roll along the inside periphery of the ring,without slipping. The spring can only be stretched or compressed along the periphery of the ring,following Hooke's law. In equilibrium,the disk is at the bottom of the ring. Assuming small displacement of the disc,the time period of oscillation of the center of mass of the disk is written as $T = \frac{2 \pi}{\omega}$. The correct expression for $\omega$ is ($g$ is the acceleration due to gravity):