Question

A non-hookian spring has force $F=-k{x}^2$, where $k$ is the spring constant and $x$ is the displacement from its unstretched position. For the system shown, a mass $m$ connected to an unstretched spring is initially at rest. If the distance upto which the spring extends before the system momentarily comes to rest is ${\left(\frac{pmg}{qk}\right)}^{1/2}$, then find $(p+q)$. Assume that all surfaces as well as the pulley are frictionless.

Answer 1

Answer: 5

$mgx\cos 60^{\circ }=\underset{0}{\overset{x}{\int }}k{x}^{2}dx$