A pendulum is hung from the roof of a sufficiently high building and is moving freely to and fro like a simple harmonic oscillator. The acceleration of the bob of the pendulum is \(20\text{ m/s}^2\) at a distance of \(5\text{ m}\) from the mean position. The time period of oscillation is:
1. \(2\pi \text{ s}\)
2. \(\pi \text{ s}\)
3. \(2 \text{ s}\)
4. \(1 \text{ s}\)

A particle executes linear simple harmonic motion with an amplitude of of 3 cm. When the particle is at 2 cm from the mean position, the magnitude of its velocity  is equal to that of its acceleration. Then, its time period in seconds is 

1. $\sqrt{\frac{5}{\pi }}$

2.$\sqrt{\frac{5}{2\mathrm{\pi }}}$

3. $\frac{4\mathrm{\pi }}{\sqrt{5}}$

4. $\frac{2\mathrm{\pi }}{\sqrt{3}}$

A particle executes linear simple harmonic motion with amplitude of \(3~\text{cm}\). When the particle is at \(2~\text{cm}\) from the mean position, the magnitude of its velocity is equal to that of its acceleration. Then its time period in seconds is:
1. \(\dfrac{\sqrt5}{2\pi}\)
2. \(\dfrac{4\pi}{\sqrt5}\)
3. \(\dfrac{4\pi}{\sqrt3}\)
4. \(\dfrac{\sqrt5}{\pi}\)

A body of mass \(m\) is attached to the lower end of a spring whose upper end is fixed. The spring has negligible mass. When the mass \(m\) is slightly pulled down and released, it oscillates with a time period of \(3~\text{s}\). When the mass \(m\) is increased by \(1~\text{kg}\), the time period of oscillations becomes \(5~\text{s}\). The value of \(m\) in \(\text{kg}\) is:
1. \(\dfrac{3}{4}\)
2. \(\dfrac{4}{3}\)
3. \(\dfrac{16}{9}\)
4. \(\dfrac{9}{16}\)