A particle is executing simple harmonic motion with amplitude $A$. At a distance ' $x$ ' from the mean position, when the particle is moving towards extreme position it receives a blow in the direction of motion which instantaneously doubles its velocity. The new amplitude of the particle is

(Frequency is constant during the motion)

If the displacement ' $x$ ' of a body in motion in terms of time ' $t$ ' is given by $x=A \sin (\omega t+\theta)$, then the minimum time at which the displacement becomes maximum is

If the maximum velocity and maximum acceleration of a particle executing simple harmonic motion are respectively $5 \mathrm{~ms}^{-1}$ and $10 \mathrm{~ms}^{-2}$, then the time period of oscillation of the particle is

A body of mass 1 kg is suspended from a spring of force constant $600 \mathrm{Nm}^{-1}$. Another body of mass 0.5 kg moving vertically upwards hits the suspended body with a velocity of $3 \mathrm{~ms}^{-1}$ and embedded in it. The amplitude of motion is