Periodic and Oscillatory Motions

Electrons moving with different speeds enter a uniform magnetic field in a direction perpendicular field. They will move along circular paths, time periods of rotation will be :

A particle is fastened at the end of a string and is whirled in a vertical circle with the other end of the string being fixed. The motion of the particle is,

Consider the earth as a homogeneous sphere of radius $R$ and a straight hole is bored in it through its centre. Show that a particle dropped into the hole will execute a simple harmonic motion such that its time period is $T=2\mathrm{\pi }\sqrt{\frac{\mathrm{R}}{\mathrm{g}}}$.

A body is vibrating in simple harmonic motion. If its acceleration is $12 \mathrm{cm} {\mathrm{s}}^{-2}$ at a displacement $3 \mathrm{cm},$ then time period is

Find the time period of the body (mass $m$), shown in the figure, when displaced slightly in the vertical direction. 

Define periodic motion

An air chamber of volume $V$ has a neck of cross-sectional area $a$ into which a light ball of mass $m$ just fits and can move up and down without friction. The diameter of the ball is equal to that of the neck of the chamber. The ball is pressed down a little and released. If the bulk modulus of air is $B$, the time period of the oscillation of the ball is

The circular motion of a particle with constant speed is

Two small magnets have their masses and lengths in the ratio 1 : 2. The maximum torques experienced by them in a uniform magnetic field are the same. For small oscillations, the ratio of their time periods is

Two masses $m_1 \text{and} m_2$ suspended together by a massless spring of spring constant K. When the masses are in equilibrium, $m_1$ is removed without disturbing the system. The angular frequency of $m_2$ is

Due to some force $F_1$ a body oscillates with period $\frac{4}{5}s$ and due to other force $F_2$ oscillates with period $\frac{3}{5}s$ . If both forces act simultaneously, the new period will be

A person is listening to a tone of 500 Hz sitting at a distance of 450 m from the source of the sound. What is the time interval between successive compressions from the source?

The frequency of power supply used in India is

A horizontal platform with an object placed on it is executing $\mathrm{S}\mathrm{H}\mathrm{M}$ in the vertical direction. The amplitude of oscillation is $2.5\mathrm{ }\mathrm{c}\mathrm{m}$ . What must be the least period of these oscillation so that the object is not detached ?

The displacement of a particle in simple harmonic motion in one time period is -

Two tuning forks of frequencies 256 and 258 vibrations/sec are sounded together, then time interval between consecutive maxima heard by the observer is

The function ${\sin }^2\left(\omega t\right)$ represents

A body is vibrating in simple harmonic motion. If its acceleration is $12 \mathrm{c}\mathrm{m}\mathrm{ }{\mathrm{s}}^{-2}$ at a displacement $3 \mathrm{cm}$, then time period is

The circular motion of a particle with constant speed is

If a simple harmonic is represented by $\frac{{\mathrm{d}}^{2}x}{\mathrm{d}{t}^2}+\alpha x=0$, its time period is