The curve between the potential energy \((U)\) and displacement \((x)\) is shown. Which of the oscillation is about the mean position, \(x = 0?\)

1.		2.
3.		4.

A spring-block system oscillates with a time period \(T\) on the earth's surface. When the system is brought into a deep mine, the time period of oscillation becomes \(T'.\) Then one can conclude that:
1. \(T'>T\)
2. \(T'<T\)
3. \(T'=T\)
4. \(T'=2T\)

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

Acceleration-time (\(a-t\)) graph for a particle performing S.H.M. is shown in the figure. Select the incorrect statement.

A simple pendulum is pushed slightly from its equilibrium towards left and then set free to execute simple harmonic motion. Select the correct graph between its velocity(\(v\)) and displacement (\(x \)).

1.		2.
3.		4.

For a particle executing simple harmonic motion, the kinetic energy is given by \(K=K_{0}cos^{2} \omega t.\) The maximum value of potential energy for the given particle: 

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