When the mass attached to a spring is increased from 4 kg to 9 kg , the time period of oscillation increases by $0.2 \pi \mathrm{~s}$. Then, the spring constant of the spring is

The kinetic energy of a particle executing simple harmonic motion at a displacement of 3 cm from the mean position is 4 mJ . If the amplitude of the particle is 5 cm , then the maximum force acting on the particle is

A body of mass 1 kg is attached to the lower end of a vertically suspended spring of force constant $600 \mathrm{~N}-\mathrm{m}^{-1}$. If another body of mass 0.5 kg moving vertically upward hits the suspended body with a velocity $3 \mathrm{~ms}^{-1}$ and embedded in it, then the frequency of the oscillation is

If the displacement $y$ (in cm ) of a particle executing simple harmonic motion is given by the equation $y=5 \sin (3 \pi t)+5 \sqrt{3} \cos (3 \pi t)$, then the amplitude of the particle is