The variation of the potential energy of the harmonic oscillator is shown in the figure. The spring constant will be:
           
1. \(1\times10^{2}~\text{N/m}\)
2. \(150~\text{N/m}\)
3. \(0.667\times10^{2}~\text{N/m}\)
4. \(3\times10^{2}~\text{N/m}\)

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. \(1~\text{s}\)

A particle is executing linear simple harmonic motion with an amplitude \(a\) and an angular frequency \(\omega\). Its average speed for its motion from extreme to mean position will be:
1. \(\frac{a\omega}{4}\)
2. \(\frac{a\omega}{2\pi}\)
3. \(\frac{2a\omega}{\pi}\)
4. \(\frac{a\omega}{\sqrt{3}\pi}\)