A-pendulum suspended from the ceiling of a train has a period T when the train is at rest. When the train accelerates with a uniform acceleration a, the period of oscillation will

• increase

• decrease

• remain unaffected

• become infinite

The motion of a particle executing SHM is given by x = 0.01sin1O0$\mathrm{\pi }$(t + 0.05), where x is in metre and t in second. The time period of
motion (in second) is

• 0.01

• 0.02

• 0.1

• 0.2

A simple pendulum has a length l and the mass of the bob is m. The bob is given a charge q coulomb. The pendulum is suspended between the vertical plates of a charged parallel plate capacitor. If E is the electric field strength between the plates, the time period of the pendulum is given by

• $2\mathrm{\pi }\sqrt{\frac{\mathrm{l}}{\mathrm{g}}}$

• $2\mathrm{\pi }\sqrt{\frac{\mathrm{l}}{\sqrt{\mathrm{g} + {\displaystyle \frac{\mathrm{qE}}{\mathrm{m}}}}}}$

• $2\mathrm{\pi }\sqrt{\frac{\mathrm{l}}{\sqrt{\mathrm{g} - {\displaystyle \frac{\mathrm{qE}}{\mathrm{m}}}}}}$

• $2\mathrm{\pi }\sqrt{\frac{\mathrm{l}}{\sqrt{{\mathrm{g}}^2 + {\left({\displaystyle \frac{qE}{\mathrm{m}}}\right)}^2}}}$

The vertical extension in a light spring by a weight of 1 kg suspended from the wire is 9.8 cm. The period of oscillation is

• 20π s

• 2π s

• $\frac{2\mathrm{\pi }}{10}\mathrm{s}$

• 200$\mathrm{\pi }$ s

A particle of mass 10 g is describing SHM along a straight line with a period of 2 s and amplitude of 10 cm. Its kinetic energy when it is at 5 cm from its equilibrium position is

• 3.75 π² erg

• 375 π² erg

• 0.375 π² erg

• 37.5 π² erg

The angular amplitude of a simple pendulum is θ₀ The maximum tension in its string will be

• mg(1 - θ₀)

• mg(1 + θ₀)

• mg(1 - ${\mathrm{\theta }}_0^2$)

• mg(1 + ${\mathrm{\theta }}_0^2$)

The graph between velocity and displacement of a particle, executing SHM is:

• a straight line

• a parabola

• a hyperbola

• an ellipse

A body executing SHM has its velocity 10 cm/s and 7 cm/s when its displacements from the mean position are 3 cm and 4 cm respectively. The length of the path is :

• 10 cm

• 9.5 cm

• 4 cm

• 11.36 cm

A particle executing simple harmonic motion has a time period of 4 sec. After how much interval of time from t = 0 will its displacement be half of its amplitude :

• 1/3 sec

• 1/2 sec

• 2/3 sec

• 1/6 sec

A particle is executing the motion x = a cos (ωt - θ). The maximum velocity of the particle is :

• aω cosθ

• aω

• aω sinθ

• none of these