The velocity-time diagram of a harmonic oscillator is shown in the figure given below. The frequency of oscillation will be:
                

1. \(25~\text{Hz}\)
2. \(50~\text{Hz}\)
3. \(12.25~\text{Hz}\)
4. \(33.3~\text{Hz}\)

A mass of 30 g is attached with two springs having spring constant 100 N/m and 200 N/m and other ends of springs are attached to rigid walls as shown in the given figure. The angular frequency of oscillation will be
                                

1.  $\frac{100}{2\mathrm{\pi }}$ $\mathrm{rad}/\mathrm{s}$

2.  $\frac{100}{\mathrm{\pi }}$ $\mathrm{rad}/\mathrm{s}$

3.  100 rad/s

4.  200$\mathrm{\pi }$ rad/s

If a particle in SHM has a time period of \(0.1\) s and an amplitude of \(6\) cm, then its maximum velocity will be:
1. \(120 \pi\)$\mathrm{}$ cm/s 
2. \(0.6 \pi\)$\mathrm{}$ cm/s 
3. \(\pi\)$\mathrm{}$ cm/s
4. \(6\) cm/s

                     
1. \(\frac{\pi}{2}~\text{s}\)
2. \(\frac{1}{2}~\text{s}\)
3. \(\pi~\text{s}\)
4. \(1~\text{s}\)

The time periods for the figures (a) and (b) are ${\mathrm{T}}_1$ $\mathrm{and}$ ${\mathrm{T}}_2$ respectively. If all surfaces shown below are smooth, then the ratio $\frac{{\mathrm{T}}_1}{{\mathrm{T}}_2}$ will be:
   

1.  1: $\sqrt{3}$

2.  1: 1

3.  2: 1

4.  $\sqrt{3}$: 2

A particle is attached to a vertical spring and pulled down a distance of 0.01 m below its mean position and released. If its initial acceleration is 0.16 $\mathrm{m}/{\mathrm{s}}^2$, then its time period in seconds will be:

1.  $\mathrm{\pi }$

2.  $\frac{\mathrm{\pi }}{2}$

3.  $\frac{\mathrm{\pi }}{4}$

4.  $2\mathrm{\pi }$