A spring is stretched by \(5~\text{cm}\) by a force \(10~\text{N}\). The time period of the oscillations when a mass of \(2~\text{kg}\) is suspended by it is:
1. \(3.14~\text{s}\)
2. \(0.628~\text{s}\)
3. \(0.0628~\text{s}\)
4. \(6.28~\text{s}\)

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. \(\frac{3}{4}\)
2. \(\frac{4}{3}\)
3. \(\frac{16}{9}\)
4. \(\frac{9}{16}\)

The time period of a mass suspended from a spring is \(T\). If the spring is cut into four equal parts and the same mass is suspended from one of the parts, then the new time period will be:
1. \(\frac{T}{4}\)
2. \(T\)
3. \(\frac{T}{2}\)
4. \(2T\)

A spring elongates by a length 'L' when a mass 'M' is suspended to it. Now a tiny mass 'm' is attached to the mass 'M' and then released. The new time period of oscillation will be:

1.  \(2 \pi \sqrt{\frac{\left(\right. M   +   m \left.\right) l}{Mg}}\)

2. \(2 \pi \sqrt{\frac{ml}{Mg}}\)

3. \(2 \pi \sqrt{L   /   g}\)

4. \(2 \pi \sqrt{\frac{Ml}{\left(\right. m   +   M \left.\right) g}}\)