The variation of kinetic energy (KE) of a particle executing simple harmonic motion with the displacement $$(x)$$ starting from mean position to extreme position (A) is given by

A particle executes S.H.M. of amplitude A along x-axis. At t = 0, the position of the particle is $$x=\frac{A}{2}$$ and it moves along positive x-axis. The displacement of particle in time t is $$x = A\sin (wt + \delta )$$, then the value of $$\delta$$ will be

For particle P revolving round the centre O with radius of circular path $$\mathrm{r}$$ and angular velocity $$\omega$$, as shown in below figure, the projection of OP on the $$x$$-axis at time $$t$$ is

A mass $$m$$ is attached to two strings as shown in figure. The spring constants of two springs are $$\mathrm{K}_{1}$$ and $$\mathrm{K}_{2}$$. For the frictionless surface, the time period of oscillation of mass $$m$$ is :