I need the answer in details and ASAP The 200 lb collar show

The 20.0 lb collar, shown to the right, slides without friction along the vertical rod; spring attached to the collar has an unstretched length of 4.00 in (not shown) and a stiffness (force constant) of 3.00 lb in. If the collar is initially moving downward at point 1 with a speed of 1.00 ft s, determine the speed at which the collar is moving when it is at point 2. (Watch your units ft, lb/ft, ft/s,etc)

Solution

when moved x distance downward spring elongates by (64+x²)^1/2-4 in

force acting=3((64+x²)^1/2-4)[sin(tan^-1(x/8)]=20vdv/dx

20(v²-12²)/2=integration of 3((64+x²)^1/2-4)[sin(tan^-1(x/8)]dx for x=0 to x=6

20(v²-12²)/2=-21

v=11.912 lb/in