The displacement of a particle varies with time according to the relation
$x = a\sin\omega t + b\cos\omega t$

For a particle executing S.H.M., the potential energy is $n$ times the kinetic energy when its displacement from mean position is $\left(\dfrac{2\sqrt{2}}{3}\right)A$, where $A$ is the amplitude of S.H.M. The value of $n$ is

A particle is performing S.H.M. about $x = 0$, with an amplitude $a$ and time period $T$. The speed of the particle at $x = \dfrac{a}{3}$ will be

A simple pendulum of length $l_1$ has periodic time $2.4$ s. Another simple pendulum of length $l_2 < l_1$, has periodic time $1.8$ s. The periodic time of simple pendulum of length $(l_1 - l_2)$ is nearly