An oscillation is described by the equation $x=A\sin 2\pi {\gamma }_{1}t$ where $A$ changes with time according to the law $A=A_0\left(1+\cos 2\pi {\gamma }_{2}t\right)$ where $A_0$ is constant. Find the ratio of frequencies of harmonic oscillations forming oscillation 

A block of mass $m$ is placed on a level frictionless table. The block is attached to a horizontally aligned spring fixed with its other end is vibrating in a horizontal plane with the period $T$. Suddenly at the instant of time when the spring comes to the position of equilibrium and becomes unstretched the block disconnects from the spring and continues sliding across the frictionless surface away from the until it encounters a loop of radius $R$. What must be the amplitude of vibrations of the blocks on the spring in order for the block to complete one loop without falling down?

The displacement $y$ of a particle executing periodic motion is given by $y=4{\cos }^2 \left(\frac{t}{2}\right)\sin \left(1000t\right)$. This expression may be considered to be a result of the superposition of

A uniform cylinder of mass $m$ and length $l$ having area of cross-section a is suspended lengthwise with the help of a massless spring of constant $k$. The cylinder is half submerged in a liquid of density $\rho$. A small push and release makes it vibrate with small amplitude. The frequency of oscillation is