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

The displacement of a linear harmonic oscillator is given by $x=A \cos \omega t.$ The curves showing the variation of the potential energy with $t$ and $x$ (see figure) are displayed respectively by:

A simple pendulum has time period $T_1$. When the point of suspension moves vertically up according to the equation $y=k{t}^2$ where $k=1$ $\mathrm{m} {\mathrm{s}}^{-2}$ and $t$ is time then the time period of the pendulum is $T_2$ then ${\left(\frac{T_1}{T_2}\right)}^2$ is

The mass $M$ shown in the figure oscillates in simple harmonic motion with amplitude $A.$ The amplitude of the point $P$ is 

Assertion: The motion of a simple pendulum is simple harmonic only for  $a$$<<l$.

Reason: Motion of a simple pendulum is SHM for small angular displacement.

Assertion: pendulum clocks go slow in summer and fast in winter.

Reason: The length of the pendulum used in the clock increases in summer.

Assertion: A simple pendulum is mounted on a truck that moves with constant velocity The time period of the pendulum will increase.

Reason: The effective length of the pendulum will decrease.