A spring is stretched by 0.2 m when a mass of 0.5 kg is suspended to it. The time period of the spring when 0.5 kg mass is replaced with a mass of 0.25 kg is suspended to it is
(Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )
A body of mass 4 kg attached to a spring of force constant $64 \mathrm{Nm}^{-1}$ executes simple harmonic motion on a frictionless horizontal surface. The time period of oscillation is
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
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