The equation of motion of a particle is \({d^2y \over dt^2}+Ky=0 \) where \(K\) is a positive constant. The time period of the motion is given by: 

1.	\(2 \pi \over K\)	2.	\(2 \pi K\)
3.	\(2 \pi \over \sqrt{K}\)	4.	\(2 \pi \sqrt{K}\)

The kinetic energy of a particle executing SHM is 16 J when it is in its mean position. If the amplitude of oscillations is 25 cm and the mass of the particle is 5.12 kg, the time period of its oscillation will be:
1. $\frac{\mathrm{\pi }}{5}sec$ 
2. $2\mathrm{\pi }$ $\sec$
3. $20\mathrm{\pi }$ $\sec$   
4. $5\mathrm{\pi }$ $\sec$

The period of oscillation of a simple pendulum of length \(\mathrm{L}\) suspended from the roof of a vehicle which moves without friction down an inclined plane of inclination $\theta$, is given by:

1.   $2\mathrm{\pi }\sqrt{\frac{\mathrm{L}}{\mathrm{gcos\theta }}}$               

2.  $2\mathrm{\pi }\sqrt{\frac{\mathrm{L}}{\mathrm{gsin}\theta }}$

3.  $2\mathrm{\pi }\sqrt{\frac{\mathrm{L}}{\mathrm{g} }}$                     

4. $2\mathrm{\pi }\sqrt{\frac{\mathrm{L}}{\mathrm{gtan\theta }}}$

On a smooth inclined plane, a body of mass \(M\) is attached between two springs. The other ends of the springs are fixed to firm supports. If each spring has force constant \(K\), the period of oscillation of the body (assuming the springs as massless) will be:
                
1. \(2\pi \left( \frac{M}{2K}\right)^{\frac{1}{2}}\)
2. \(2\pi \left( \frac{2M}{K}\right)^{\frac{1}{2}}\)
3. \(2\pi \left(\frac{Mgsin\theta}{2K}\right)\)
4. \(2\pi \left( \frac{2Mg}{K}\right)^{\frac{1}{2}}\)

An ideal spring with spring-constant K is hung from the ceiling and a block of mass M is attached to its lower end. The mass is released with the spring initially un-stretched. Then the maximum extension in the spring will be:
1. 4 Mg/K 
2. 2 Mg/K
3. Mg/K 
4. Mg/2K

The velocity-time diagram of a harmonic oscillator is shown in the figure given below. The frequency of oscillation will be:
                

1. 25 Hz
2. 50 Hz
3. 12.25 Hz
4. 33.3 Hz

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 time periods for the figures (a) and (b) are ${\mathrm{T}}_1$ $\mathrm{and}$ ${\mathrm{T}}_2$ respectively. If all surfaces shown below are smooth, then the ratio $\frac{{\mathrm{T}}_1}{{\mathrm{T}}_2}$ will be:
   

1.  1: $\sqrt{3}$

2.  1: 1

3.  2: 1

4.  $\sqrt{3}$: 2

A particle is attached to a vertical spring and pulled down a distance of 0.01 m below its mean position and released. If its initial acceleration is 0.16 $\mathrm{m}/{\mathrm{s}}^2$, then its time period in seconds will be:

1.  $\mathrm{\pi }$

2.  $\frac{\mathrm{\pi }}{2}$

3.  $\frac{\mathrm{\pi }}{4}$

4.  $2\mathrm{\pi }$