physics
posted by Mel .
A 5 kg block is placed near the top of a frictionless ramp, which makes an angle of 30o degrees to the horizontal. A distance d = 1.3 m away from the block is an unstretched spring with k = 3000 N/m. The block slides down the ramp and compresses the spring. Find the magnitude of the maximum compression of the spring.
xmax=?

Use conservation of energy.
At the top of the ramp and end of compression, the kinetic energy is zero, so
Initial gravity P.E. = Final spring P.E.
M g d sin30 = (1/2) k Xmax^2
Solve for Xmax 
.146

0.15419320656221194

.145679

you must account for the distance the spring compresses as well as the 1.3m the block travels the final equation will turn out to be a quadratic