The frequency of a simple pendulum in a free-falling lift will be:
1. zero
2. infinite
3. can't say
4. finite

When a mass is suspended separately by two different springs, in successive order, then the time period of oscillations is \(t _1\) and \(t_2\) respectively. If it is connected by both springs as shown in the figure below, then the time period of oscillation becomes \(t_0.\) The correct relation between \(t_0,\) \(t_1\) & \(t_2\) is:

1. ${{\mathrm{t}}_0}^2={{\mathrm{t}}_1}^2+{{\mathrm{t}}_2}^2$

2. ${{\mathrm{t}}_0}^{-2}={{\mathrm{t}}_1}^{-2}+{{\mathrm{t}}_2}^{-2}$

3. ${{\mathrm{t}}_0}^{-1}={{\mathrm{t}}_1}^{-1}+{{\mathrm{t}}_2}^{-1}$

4. ${\mathrm{t}}_0={\mathrm{t}}_1+{\mathrm{t}}_2$

When an oscillator completes 100 oscillations, its amplitude is reduced to $\frac{1}{3}$ of the initial value. What will be its amplitude, when it completes 200 oscillations?

1. $\frac{1}{8}$

2. $\frac{2}{3}$

3. $\frac{1}{6}$

4. $\frac{1}{9}$

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 particle of mass \(m\) oscillates with simple harmonic motion between points \(x_1\) and \(x_2\), the equilibrium position being \(O\). Its potential energy is plotted. It will be as given below in the graph:

1.		2.
3.		4.

In case of a forced vibration, the resonance wave becomes very sharp when the:
1. Damping force is small
2. Restoring force is small
3. Applied periodic force is small
4. Quality factor is small

The potential energy of a simple harmonic oscillator, when the particle is halfway to its endpoint, will be:
1. \(\frac{2E}{3}\)
2. \(\frac{E}{8}\)
3. \(\frac{E}{4}\)
4. \(\frac{E}{2}\)

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