A simple pendulum is oscillating without damping. When the displacement of the bob is less than maximum, its acceleration vector $\overrightarrow{a}$ is correctly shown in: 

1.		2.
3.		4.

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

There is a simple pendulum hanging from the ceiling of a lift. When the lift is stand still, the time period of the pendulum is T. If the resultant acceleration becomes g/4, then the new time period of the pendulum is 

(1) 0.8 T

(2) 0.25 T

(3) 2 T

(4) 4 T

A block P of mass m is placed on a frictionless horizontal surface. Another block Q of same mass is kept on P and connected to the wall with the help of a spring of spring constant k as shown in the figure. μ_s is the coefficient of friction between P and Q. The blocks move together performing SHM of amplitude A. The maximum value of the friction force between P and Q will be:

1. kA

2.  $\frac{kA}{2}$

3. Zero

4. μ_s mg

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 

Two simple pendulums have time periods T and $\frac{5T}{4}$. They start vibrating at the same instant from the mean position in the same phase. The phase difference between them when bigger pendulum completes one oscillation will be:

1. $\frac{\mathrm{\pi }}{6}$

2. $\frac{\mathrm{\pi }}{4}$

3. $\frac{\mathrm{\pi }}{3}$

4. $\frac{\mathrm{\pi }}{2}$

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

A body mass m is attached to the lower end of a spring whose upper end is fixed. The spring has neglible mass. When the mass m is slightly pulled down and released, it oscillates with a time period of 3s. When the mass m is increased by 1 kg, the time period of oscillations becomes 5s. The value of m in kg is-

(1) $\frac{3}{4}$               

(2)$\frac{4}{3}$

(3) $\frac{16}{9}$               

(4) $\frac{9}{16}$

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