The displacement of a particle is given by the relation $x=4(\cos \pi t+\sin \pi t)$. The amplitude of the particle is

The displacement of a particle executing simple harmonic motion is given by $x=2 \cos (t)$ where $t$ is the time in seconds then the time period of the particle is

A force of 6.4 N stretches a vertical spring by 0.1 m . If it were to oscillate with a period of $\pi / 4$, then the mass that is to be suspended from the spring is

A pendulum has a time period $T$ in air. Whạt it is made to oscillate in water its time period is $\sqrt{2} T$. Then the relative density of the material of the bob of the pendulum is (neglect damping)