Kinetic energy of a particle executing simple harmonic motion in straight line is \(pv^2\) and potential energy is \(qx^2,\) where \(v\) is speed at distance \(x\) from the mean position. The time period of the SHM is given by the expression:

1. $2\mathrm{\pi }\sqrt{\frac{\mathrm{q}}{\mathrm{p}}}$

2. $2\mathrm{\pi }\sqrt{\frac{p}{q}}$

3. $2\mathrm{\pi }\sqrt{\frac{\mathrm{q}}{\mathrm{p}+\mathrm{q}}}$

4. $2\mathrm{\pi }\sqrt{\frac{p}{p+q}}$

The amplitude and the time period in an S.H.M. are 0.5 cm and 0.4 sec respectively. If the initial phase is $\mathrm{\pi }/2$ radian, then the equation of S.H.M. will be:

1. $\mathrm{y}=0.5\sin 5\mathrm{\pi t}$

2. $\mathrm{y}=0.5\sin 4\mathrm{\pi t}$

3. $\mathrm{y}=0.5\sin 2.5\mathrm{\pi t}$

4. $\mathrm{y}=0.5\cos 5\mathrm{\pi t}$

In simple harmonic motion, the ratio of acceleration of the particle to its displacement at any time is a measure of:

One end of a spring of force constant \(\mathrm{k}\) is fixed to a vertical wall and the other to a block of mass \(\mathrm{m}\) resting on a smooth horizontal surface. There is another wall at a distance ${\mathrm{x}}_0$ from the block. The spring is then compressed by $2{\mathrm{x}}_0$ and then released. The time taken to strike the wall will be?

When the displacement is half the amplitude in an SHM, the ratio of potential energy to the total energy is:
1. 1 / 2

2. 1 / 4

3. 1

4. 1 / 8

A block is connected to a relaxed spring and kept on a smooth floor. The block is given a velocity towards the right. Just after this:
               

A simple pendulum of mass m swings about point B between extreme positions A and C. Net force acting on the bob at these three points is correctly shown by:

1.		2.
3.		4.

The potential energy of a particle oscillating along the x-axis is given as U = 20+ (x–2)² where U is in joules and x in meters. The total mechanical energy of the particle is 36 J. The maximum kinetic energy of the particle will be:
1. 24 J 

2. 36 J

3. 16 J 

4. 20 J

A particle is executing SHM according to y = a cos$\mathrm{\omega t}$. Then, which of the following graphs represent variations of potential energy?
             
1. I and III

2. II and IV

3. II and III

4. I and IV

Two springs, of force constants k₁ and k₂ are connected to a mass m as shown in the figure. The frequency of oscillation of the mass is f. If both k₁ and k₂ are made four times their original values, the frequency of oscillation will become: