The variation of acceleration, \(a~\) of a particle executing SHM with displacement \(x~\) is:

1.		2.
3.		4.

The motion of a particle varies with time according to the relation $\mathrm{y}$ $=\mathrm{a}$ $\sin$ $\mathrm{\omega t}+\mathrm{a}$ $\cos$ $\mathrm{\omega t}$. Then:

 The displacement of a particle executing SHM is given by y = 0.25 (sin 200t) cm. The maximum speed of the particles is:

1.  200 cm/sec

2.  100 cm/sec

3.  50 cm/sec

4.  0.25 cm/sec

A particle undergoes SHM with a time period of 2 seconds. In how much time will it travel from its mean position to a displacement equal to half of its amplitude?

(1) $\frac{1}{2}s$

(2) $\frac{1}{6}s$

(3) $\frac{1}{4}s$

(4) $\frac{1}{3}s$

A second's pendulum is mounted in a rocket. Its period of oscillation decreases when the rocket:

(1) Comes down with uniform acceleration

(2) Moves around the earth in a geostationary orbit

(3) Moves up with a uniform velocity

(4) Moves up with the uniform acceleration

A small sphere carrying a charge ‘q’ is hanging in between two parallel plates by a string of length L. Time period of pendulum is T₀. When parallel plates are charged, the electric field between the plates is E and time period changes to T. The ratio T/T₀ is equal to 

(1) ${\left(\frac{{\displaystyle g+\frac{{\displaystyle qE}}{{\displaystyle m}}}}{{\displaystyle g}}\right)}^{1/2}$           (2) ${\left(\frac{{\displaystyle g}}{{\displaystyle g+\frac{{\displaystyle qE}}{{\displaystyle m}}}}\right)}^{3/2}$

(3) ${\left(\frac{{\displaystyle g}}{{\displaystyle g+\frac{{\displaystyle qE}}{{\displaystyle m}}}}\right)}^{1/2}$           (4) None of these 

A simple pendulum has a time period ${\mathrm{T}}_1$ when on the earth’s surface, and ${\mathrm{T}}_2$ when taken to a height R above the earth’s surface, where R is the radius of the earth. The value of ${\mathrm{T}}_2/{\mathrm{T}}_1$ is:

1. 1

2. $\sqrt{2}$

3. 4

4. 2

A particle executes linear simple harmonic motion with an amplitude of of 3 cm. When the particle is at 2 cm from the mean position, the magnitude of its velocity  is equal to that of its acceleration. Then, its time period in seconds is 

(a) $\sqrt{\frac{5}{\pi }}$

(b)$\sqrt{\frac{5}{2\mathrm{\pi }}}$

(c)$\frac{4\mathrm{\pi }}{\sqrt{5}}$

(d)$\frac{2\mathrm{\pi }}{\sqrt{3}}$

When two displacements represented by y₁=asin(ωt) and y₂=bcos(ωt) are superimposed,the motion is -

(1) not a simple harmonic

(2) simple harmonic with amplitude a/b

(3) simple harmonic with amplitude $\sqrt{a^{2 }+ b^2}$

(4) simple harmonic with amplitude (a+b)/2

The displacement of a particle along the x-axis is given by $x=a{\sin }^2$ $\omega t$. The motion of the particle corresponds to: