Spring energy question

Suppose a 300g mass is dropped from a height of 40cm onto a vertical spring with spring constant 200N/m (having a light platform on top) and sticks to the platform (a) How far will the spring compress? (b) How far will the spring be stretched as the mass and spring rebound? use S.I. units.
I can do part (a) ans = .124m. For part (b) I cannot get right answer =.095m

Us at the bottom = Ug at end

where: Us = potential energy of the spring
Ug = potential energy of gravity

this gives:

.5kx^2 = mgx
=> .5kx = mg
= wrong result
what am I missing,
Thanks & regards
 

OlderDan

Science Advisor
Homework Helper
3,021
1
If you have done part a) correctly, you know the lowest point of the motion of the mass attached to the spring. If you find the equilibrium point, you can treat the rest of the problem as a harmonic oscillator with an initial displacement starting with zero velocity.
 

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