A particle is executing simple harmonic motion with a time period $T$.  At time $t=0$, it is at its position of equilibrium. The kinetic energy-time graph of the particle will look like :

Two masses $\mathrm{m}$ and $\frac{\mathrm{m}}{2}$ are connected at the two ends of a massless rigid rod of length $\ell$. The rod is suspended by a thin wire of torsional constant $k$ at the centre of mass of the rod-mass system (see figure). Because of torsional constant$k,$the restoring torque is $\tau =k\theta$. for angular displacement $\theta .$ If the rod is rotated by $\theta$  and released, the tension in it when it passes through its mean position will be : 

A highly rigid cubical block $A$ of small mass $M$ and side $L$ is fixed rigidly on to another cubical block $B$ of the same dimensions and of low modulus of rigidity $\eta$ such that the lower face of $A$ completely covers the upper face of $B$. The lower face of $B$ is rigidly held on a horizontal surface. A small force $F$ is applied perpendicular to one of the side faces of $A$. After the force is withdrawn, block $A$ executes small oscillations, the time-period of which is given by

A cylindrical piston of mass $M$ slides smoothly inside a long cylinder closed at one end, enclosing a certain mass of a 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 (process is isothermal)

A U-tube contains mercury of total length $2l$ as shown and is disturbed so that it oscillates back and forth from arm to arm. If we neglect friction, the period of oscillation is: