Physics Question on Oscillations

Question

A mass of $2.0\, kg$ is put on a flat pan attached to a vertical spring fixed on the ground as shown in the figure. The mass of the spring and the pan is negligible. When pressed slightly and released the mass executes a simple harmonic motion . The spring constant is $200\, N/m$ . What should be the minimum amplitude of the motion so that the mass gets detached from the pan (take $g = 10 \,m /s^2$ ).

Answer 1

Solution

For given conditions $m g=m \omega^{2} \,a-k a$
$\Rightarrow a =\frac{ mg }{ k }=\frac{2 \times 10}{200}=0.1=10 \,cm$