Equations of motion in the same direction are given by

$$\begin{gathered} {\mathrm{y}}_1 =2\mathrm{\alpha } \sin \left(\mathrm{\omega t} -\mathrm{kx}\right) \\ {\mathrm{y}}_2 =2\mathrm{\alpha } \sin \left(\mathrm{\omega t} -\mathrm{kx}-\mathrm{\theta }\right) \end{gathered}$$

The amplitude of the medium particle will be

• $2\mathrm{\alpha } \mathrm{cos\theta }$

• $\sqrt{2}\mathrm{\alpha } \mathrm{cos\theta }$

• $4\mathrm{\alpha } \cos \frac{\mathrm{\theta }}{2}$

• $\sqrt{2}\mathrm{\alpha } \cos \frac{\mathrm{\theta }}{2}$

If x, v and a denote the displacement, the velocity and the acceleration of a particle executing simple harmonic motion of time period T, then, which of the following does not change with time?

The displacement of an object attached to a spring and executing simple harmonic motion is given by x = 2 × 10^-2 cos πt metres. The time at which the maximum speed first occurs

A particle of mass m executes simple harmonic motion with amplitude ‘a’ and frequency ‘ν’. The average kinetic energy during its motion from the position of equilibrium to the end is

A coin is placed on a horizontal platform which undergoes vertical simple harmonic motion of angular frequency ω. The amplitude of oscillation is gradually increased. The coin will leave contact with the platform for the first time

The function sin²(ωt) represents