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 variation of the potential energy of the harmonic oscillator is shown in the figure. The spring constant will be:
           

A particle moves according to the law, $\mathrm{x}=\mathrm{r}$ $\cos \frac{\mathrm{\pi t}}{2}$. The distance covered by it in the time interval between t =0 to t =3 s will be:

A mass of 30 g is attached with two springs having spring constant 100 N/m and 200 N/m and other ends of springs are attached to rigid walls as shown in the given figure. The angular frequency of oscillation will be
                                

1.  $\frac{100}{2\mathrm{\pi }}$ $\mathrm{rad}/\mathrm{s}$

2.  $\frac{100}{\mathrm{\pi }}$ $\mathrm{rad}/\mathrm{s}$

3.  100 rad/s

4.  200$\mathrm{\pi }$ rad/s

If a particle in SHM has a time period of \(0.1\) s and an amplitude of \(6\) cm, then its maximum velocity will be:
1. \(120 \pi\)$\mathrm{}$ cm/s 
2. \(0.6 \pi\)$\mathrm{}$ cm/s 
3. \(\pi\)$\mathrm{}$ cm/s
4. \(6\) cm/s