$A$ particle executes linear $S.H.M.$ with amplitude $4 \ cm$. The magnitude of velocity and acceleration is equal when it is at $3 \ cm$ from the mean position. The time period of oscillation is:

$A$ ball is rolling without slipping in a spherical shallow bowl (radius $R$) as shown in the figure and is executing simple harmonic motion. If the radius of the ball is doubled,then the time period of oscillation

$A$ particle is placed at the lowest point of a smooth wire frame in the shape of a parabola,lying in the vertical $xy-$ plane having equation $x^2 = 5y$ ($x, y$ are in meters). After a slight displacement,the particle is set free. Find the angular frequency of oscillation in $rad/s$ (take $g = 10 \ m/s^2$).

$A$ small spherical ball of radius '$r$' is rolling on a curved surface which is frictionless and has a radius of curvature '$R$'. Its motion is simple harmonic. Then its time period of oscillation is proportional to ($g=$ acceleration due to gravity).

$A$ rod of mass $m$ and length $l$ is suspended from the ceiling with two strings of length $l$ as shown. When the rod is given a small push in the plane of the page and released,the time period is $T_1$. When the rod is given a push perpendicular to the plane,the time period of oscillation is $T_2$. The ratio $\frac{T_1^2}{T_2^2}$ is

$A$ cylindrical piston of mass $M$ slides smoothly inside a long cylinder closed at one end,enclosing a certain mass of gas. The cylinder is kept with its axis horizontal. If the piston is disturbed from its equilibrium position,it oscillates simple harmonically. The period of oscillation will be