Question

What spring constant k would you need to have a 3 kg mass oscillate on the spring with the same period T as the mass would have hanging from a simple pendulum of length of 0.5 meters

Answer 1

$\mathrm{Time\ period\ for\ Pendulum = T_P = 2\pi \sqrt \frac{L}{g}}$

$\mathrm{T_P = 2\pi \sqrt \frac{0.5}{9.8}}$

$\mathrm{Time\ period\ for\ Spring\ Mass\ system = T_s = 2\pi \sqrt \frac{m}{K}}$

$\mathrm{T_s = 2\pi \sqrt \frac{3}{k}}$

$\mathrm{Equating,\ T_s = T_p , \ \ \Rightarrow \ \ 2\pi \sqrt \frac{3}{k} =2\pi \sqrt \frac{0.5}{9.8} }$

$\mathrm{\frac{3}{k} = \frac{0.5}{9.8} }$

$\mathrm{\mathbf{k = 58.8\ N/m} }$