$A$ rectangular block of mass '$m$' and cross-sectional area '$A$' floats on a liquid of density '$\rho$'. It is given a small vertical displacement from equilibrium, it starts oscillating with frequency ($g$ = acceleration due to gravity).

$A$ 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

One end of a $V$-tube containing mercury is connected to a suction pump and the other end to the atmosphere. The two arms of the tube are inclined to the horizontal at an angle of $45^{\circ}$ each. $A$ small pressure difference is created between the two columns when the suction pump is removed. Will the column of mercury in the $V$-tube execute simple harmonic motion? Neglect capillary and viscous forces. Find the time period of oscillation.

$A$ particle of mass $m$ is located in a one-dimensional potential field where the potential energy is given by: $V(x) = A(1 - \cos px)$, where $A$ and $p$ are constants. The period of small oscillations of the particle is

$A$ body executes simple harmonic motion under the action of a force $F_1$ with a time period $(4/5) \ s$. If the force is changed to $F_2$,it executes $SHM$ with a time period $(3/5) \ s$. If both the forces $F_1$ and $F_2$ act simultaneously in the same direction on the body,its time period (in $s$) is:

Under the influence of force $F_1$,a body oscillates with a period $T_1$,and due to another force $F_2$,the body oscillates with a period $T_2$. If both forces act simultaneously,what is the resultant period? (Consider the displacement is the same in all three cases.)