Please see the attached file for full problem description.
m = 14 kg, k = 180 N/m, d = 4 m, angle theta = 30 deg.; g = 9.8 m/s^2
a) max. Compression:
Let the max. compression be x meters.
Let us compute x more accurately by NOT assuming that x<<4.
Taking the final totally compressed level as the reference for height (and hence for P.E. calculations)
So original height = h = (x+4)*Sin (30 deg.)
We will use the conservation of energy principles to ...
The solution explains the steps taken to calculate the compressions of a box sliding down a frictionless hill to collide with a spring clearly and comprehensively.