A 5 meter, 100 N/m spring is at a 30 degree angle to the horizontal. If a 10 kg weight is placed on the spring when it is compressed 2 meters, how high will it travel?

Answer 1

The initial stored potential energy in the spring,
(1/2) k X^2,
is initial converted to 3/4 (cos 30)^2 kinetic energy of horizontal motion and 1/4 (sin 30)^2 kinetic energy of vertical motion. That means (1/8) k X^2 is available to be converted to potential energy. That tells you how far it will rise above the initially compressed position. The length of the spring doesn't matter here.

Answer 2

How do you solve for the weight's maximum height above the ground?