Two identical blocks each of mass 'M' are connected with springs of spring constant K and placed on a smooth surface as shown in the figure. When the blocks are in contact the springs are in its natural length. The collision between the masses is elastic. The frequency of vibration on disturbing the masses symmetrically in the directions of arrows and releasing them is

                 

1.  $\frac{1}{2\mathrm{\pi }}\sqrt{\frac{\mathrm{K}}{\mathrm{M}}}$

2.  $\sqrt{\frac{\mathrm{K}}{\mathrm{M}}}$

3.  $\frac{1}{4\mathrm{\pi }}\sqrt{\frac{\mathrm{K}}{\mathrm{M}}}$

4.  $\frac{1}{\mathrm{\pi }}\sqrt{\frac{\mathrm{K}}{\mathrm{M}}}$

Two mutually perpendicular simple harmonic vibrations of the same frequency superimpose on each other. The amplitude of the two vibrations is different and they are different from each other in phase. The resultant of superposition is

1.  Parabola

2.  Straight line

3.  Elliptical

4.  Circular

Two equations of S.H.M. are ${\mathrm{y}}_1=\mathrm{asin}(\mathrm{\omega t}-\mathrm{\alpha })$ and ${\mathrm{y}}_2=\mathrm{bcos}(\mathrm{\omega t}-\mathrm{\alpha })$. The phase difference between the two is:
1. \(0^\circ\)
2. \(\alpha^\circ\)
3. \(90^\circ\)
4. \(180^\circ\)

A ring of radius R is hung by a nail on its periphery such that it can freely rotate in its vertical plane. The time period of the ring for small oscillations is:

1.  $\mathrm{T} = 2\mathrm{\pi }\sqrt{\frac{\mathrm{R}}{\mathrm{g}}}$

2.  $\mathrm{T} = \mathrm{\pi }\sqrt{\frac{\mathrm{R}}{\mathrm{g}}}$

3.  $\mathrm{T} = 2\mathrm{\pi }\sqrt{\frac{2\mathrm{R}}{\mathrm{g}}}$

4.  $\mathrm{T} = 2\mathrm{\pi }\sqrt{\frac{3\mathrm{R}}{5\mathrm{g}}}$

If the potential energy U (in J) of a body executing SHM is given by U = 20 + 10 (${\sin }^2$100$\mathrm{\pi }$t), then the minimum potential energy of the body will be:

The equation of S.H.M. is given as x = Asin(0.02$\mathrm{\pi t}$), where t is in seconds. With what time period the potential energy oscillates? 

1.  200 s

2.  100 s

3.  50 s

4.  10 s

In a stationary lift, a spring-block system oscillates with a frequency \(f.\) When the lift accelerates, the frequency becomes \(f'\) . Then:

The kinetic energy (K) of a simple harmonic oscillator varies with displacement (x) as shown. The period of the oscillation will be: (mass of oscillator is 1 kg)

The equation of an SHM is given as y=3sinωt + 4cosωt where y is in centimeters. The amplitude of the SHM will be?

The equation of a SHM is given as $\mathrm{x} = 5\sin \left(4\mathrm{\pi t} + \frac{\mathrm{\pi }}{3}\right)$, where \(\mathrm t\) is in seconds and \(\mathrm x\) in meters. During a complete cycle, the average speed of the oscillator is:
1. zero
2. \(10\) m/s 
3. \(20\) m/s
4. \(40\) m/s