The frequency of oscillation of a mass $m$ suspended by a spring is $v_1$. If the length of the spring is cut to half, the same mass oscillates with frequency $v_2$. The value of $v_2 / v_1$ is $\_\_\_\_$ .

A spring stretches by 2 mm when it is loaded with a mass of 200 g . From equilibrium position the mass is further pulled down by 2 mm and released. The frequency associated with the system and maxmimum energy in the spring are $\_\_\_\_$ Hz and $\_\_\_\_$ J, respectively.

(Take $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$ )

A particle is executing simple harmonic motion. Its amplitude is $A$ and time period is 5 sec . The time required by it to move from $x=A$ to $x=\frac{A}{\sqrt{2}}$ is $\_\_\_\_$ sec.

$$ \text { Match List - I with List - II. } $$

$$ \text { List - I } $$		$$ \text { List - II } $$
A.	$$ \sin ^2 \omega t $$	I.	Periodic with time period $T=\frac{\pi}{\omega}$ but not simple harmonic motion (SHM)
B.	$$ \sin ^3(2 \omega t) $$	II.	Periodic with time period $T=\frac{2 \pi}{\omega}$ but Not SHM
C.	$$ \sin (\omega t)+\cos (\pi \omega t) $$	III.	Periodic with time period $T=\frac{\pi}{\omega}$ and SHM
D.	$$ \cos \omega t+\cos 2 \omega t $$	IV.	Non-periodic

Choose the correct answer from the options given below :