Question

If both systems have the same mass, what is the ratio of their spring constants?
http://session.masteringphysics.com/problemAsset/1070609/5/14.P33.jpg

Answer 1

The time period for A is 4 sec. and for B is 6 sec. For spring mass system,
\[T=2\pi\sqrt\frac{m}{K}\] Since mass is same, you have:\[\frac{T_A}{T_B}=\sqrt\frac{K_B}{K_A}\]or,\[\frac{K_A}{K_B}=\frac{{T_B}^2}{{T_A}^2}\frac{36}{16}=\frac{9}{4}\]

Answer 2

A slight error in my above reply: I missed "=" just before '36/16'..