The displacement \( x\) of a particle varies with time \(t\) as \(x = A sin\left (\frac{2\pi t}{T} +\frac{\pi}{3} \right)\)$\mathrm{}$. The time taken by the particle to reach from \(x = \frac{A}{2} \) to \(x = -\frac{A}{2} \) will be:

1.	\(\frac{T}{2}\)	2.	\(\frac{T}{3}\)
3.	\(\frac{T}{12}\)	4.	\(\frac{T}{6}\)

Force on a particle F varies with time t as shown in the given graph. The displacement x vs time t graph corresponding to the force-time graph will be:
          

1.		2.
3.		4.

A particle executes linear SHM between \(x=A.\) The time taken to go from \(0\) to \(A/2\) is ${\mathrm{T}}_1$ and to go from \(A/2\) to \(A\) is ${\mathrm{T}}_2$, then:

Two simple pendulums of length 1 m and 16 m are in the same phase at the mean position at any instant. If T is the time period of the smaller pendulum, then the minimum time after which they will again be in the same phase will be:

1.  $\frac{3\mathrm{T}}{2}$

2.  $\frac{3\mathrm{T}}{4}$

3.  $\frac{2\mathrm{T}}{3}$

4.  $\frac{4\mathrm{T}}{3}$

A particle executes SHM with a time period of 4 s. The time taken by the particle to go directly from its mean position to half of its amplitude will be:

1.  $\frac{1}{3}$ s

2.  1 s

3.  $\frac{1}{2}$ s

4.   2 s

The graph between the velocity (v) of a particle executing S.H.M. and its displacement (x) is shown in the figure. The time period of oscillation for this SHM will be

1.  $\sqrt{\frac{\mathrm{\alpha }}{\mathrm{\beta }}}$

2.  $2\mathrm{\pi }\sqrt{\frac{\mathrm{\alpha }}{\mathrm{\beta }}}$

3.  $2\mathrm{\pi }\left(\frac{\mathrm{\beta }}{\mathrm{\alpha }}\right)$

4.  $2\mathrm{\pi }\left(\frac{\mathrm{\alpha }}{\mathrm{\beta }}\right)$

A simple pendulum attached to the ceiling of a stationary lift has a time period of 1 s. The distance y covered by the lift moving downward varies with time as y = 3.75 ${\mathrm{t}}^2$, where y is in meters and t is in seconds. If g = 10 $\mathrm{m}/{\mathrm{s}}^2$, then the time period of the pendulum will be:

The time period of the spring-mass system depends upon:

Acceleration of the particle at $t=\frac{8}{\mathrm{3 }}$s from the given displacement (y) versus time (t) graph will be?
                 

1. $\frac{\sqrt{3}{\mathrm{\pi }}^2}{4}$ $cm/s^2$

2. $-\frac{\sqrt{3}{\mathrm{\pi }}^2}{4}$ $cm/s^2$

3. $-{\mathrm{\pi }}^2$ $\mathrm{cm}/{\mathrm{s}}^2$

4. Zero

Equation of a simple harmonic motion is  given by x = asin$\mathrm{\omega }$t. For which value of x, kinetic energy is equal to the potential energy?

1.  $\mathrm{x}$ $=$ $\pm$ $\mathrm{a}$

2.  $\mathrm{x}$ $=$ $\pm$ $\frac{\mathrm{a}}{2}$

3.  $\mathrm{x}$ $=$ $\pm$ $\frac{\mathrm{a}}{\sqrt{2}}$

4.  $\mathrm{x}$ $=$ $\pm$ $\frac{\sqrt{3}\mathrm{a}}{2}$