physics imperfect spring
posted by annie .
The force required to compress an imperfect horizontal spring an amount x is given by F= 150x+12x^3, where x is in meters and F in newtons.
If the spring is compressed 2.1 m, what speed will it give to a 4.0 kg ball held against it and then released?

Work done = integral F dx
= 150 x^2/2 + 12 x^4/4
= 75 x^2 + 3 x^4
=75 (2.1)^2 + 3 (2.1)^4
= 389 Joules
= (1/2) m v^2