The phase difference between displacement and acceleration of a particle in a simple harmonic motion is:
1. \(\dfrac{3\pi}{2}\text{rad}\)
2. \(\dfrac{\pi}{2}\text{rad}\)
3. zero
4. \(\pi ~\text{rad}\)

The average velocity of a particle executing SHM in one complete vibration is:
1. zero
2. \(\dfrac{A \omega}{2}\)
3. \(A \omega\)
4. \(\dfrac{A \left(\omega\right)^{2}}{2}\)

The distance covered by a particle undergoing SHM in one time period is: (amplitude \(= A\))
1. zero
2. \(A\)
3. \(2 A\)
4. \(4 A\)

A particle executes linear simple harmonic motion with amplitude of \(3~\text{cm}\). When the particle is at \(2~\text{cm}\) from the mean position, the magnitude of its velocity is equal to that of its acceleration. Then its time period in seconds is:
1. \(\dfrac{\sqrt5}{2\pi}\)
2. \(\dfrac{4\pi}{\sqrt5}\)
3. \(\dfrac{4\pi}{\sqrt3}\)
4. \(\dfrac{\sqrt5}{\pi}\)

A particle is executing a simple harmonic motion. Its maximum acceleration is \(\alpha\) and maximum velocity is \(\beta.\) Then its time period of vibration will be:
1. \(\dfrac {\beta^2}{\alpha^2}\)
2. \(\dfrac {\beta}{\alpha}\)
3. \(\dfrac {\beta^2}{\alpha}\)
4. \(\dfrac {2\pi \beta}{\alpha}\)

When two displacements are represented by \(y_1 = a \text{sin}(\omega t)\) and \(y_2 = b\text{cos}(\omega t)\) are superimposed, then the motion is:

A particle is executing SHM along a straight line. Its velocities at distances \(x_1\) and \(x_2\) from the mean position are \(v_1\) and \(v_2\), respectively. Its time period is: