Draw the Graph between Applied Force and Force of Friction.

The potential energy of a particle oscillating in $X$-axis is given as $U= 40 +{(x-2)}^2$, where $U$ and $x$ are measured in Joules and metres. Total mechanical energy of the particle is $50 \mathrm{J}$.

Find its maximum kinetic energy.

The resultant amplitude due to superposition of three simple harmonic motions $x_1=3\sin \omega t,x_2=5\sin (\omega t+37°) and x_3-15\cos \omega t.$

A particle executes simple harmonic motion between $x=-A$ and $x=+A$. The time taken by it to go from $0$ to $\frac{A}{2}$ is $T_1$ and to go from $\frac{A}{2}$ to $A$ is $T_2$. Then

Three simple harmonic motions in the same direction having the same amplitude $a$ and same period are superposed. If each differs in phase from the next by $45°$, then

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 After the force is withdrawn, block $A$ executes small oscillations, the time-period of which is given by