The block shown in figure is released from rest and initially the spring is at its natural length. Write down the energy conservation equation. When the spring is compressed by `l_(1)`?

Explanation

Here two conservative forces are included in the problem
(i) Gravitational force (ii) spring force
we assume zero gravitational potential energy
at A as shown in figure.
from mechanical energy conservation
`k_(f) + u_(f) = k_(i) + u_(i)` ....(i)
`(1)/(2) mv^(2) + (1)/(2) k l_(1)^(2) ` = mg (`l_(1) + l`) sin `theta`