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 mass m is suspended from two springs of spring constant $k_1$ $and$ $k_2$ as shown in the figure below. The time period of vertical oscillations of the mass will be
                

1. $2\mathrm{\pi }\sqrt{\left(\frac{{\mathrm{k}}_1+{\mathrm{k}}_2}{\mathrm{m}}\right)}$

2. $2\mathrm{\pi }\sqrt{\frac{\mathrm{m}}{\left({\mathrm{k}}_1+{\mathrm{k}}_2\right)}}$

3. $2\mathrm{\pi }\sqrt{\frac{\mathrm{m}\left({\mathrm{k}}_1{\mathrm{k}}_2\right)}{\left({\mathrm{k}}_1+{\mathrm{k}}_2\right)}}$

4. $2\mathrm{\pi }\sqrt{\frac{\mathrm{m}\left({\mathrm{k}}_1+{\mathrm{k}}_2\right)}{\left({\mathrm{k}}_1{\mathrm{k}}_2\right)}}$

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?

Which one of the following is not an example of simple harmonic motion?

A mass is connected to a spring and it vibrates up and down, forming a simple harmonic system. Which of the following is/are correct?

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

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

The angular velocities of three bodies in simple harmonic motion are ${\omega }_1,$ ${\omega }_2,$ ${\omega }_3$ with their respective amplitudes as $A_1,$ $A_2,$ $A_3$. If all the three bodies have the same mass and maximum velocity, then:

The total energy of a particle, executing simple harmonic motion is:

1. $\propto$ $x$                 

2. $\propto$ $x^2$

3.  Independent of x 

4.  $\propto$ $x^{1/2}$