A 1.82 kg box moves back and forth on a horizontal frictionless surface between two different springs, as shown. The box is initially pressed against the stronger spring (k1 = 37.0 N/cm), compressing it 3.10 cm, and then is released from rest. By how much will the box compress the weaker spring (k2 = 18.5 N/cm)?

Question

I tried using Uel=1/2 kx^2 to determine the potential force from spring1. And I used that force to spring2 again using U=1/2 kx^2 to determine x, but the answer was wrong.

Answer 1

U1=(1/2)(37.0)N/cm (3.10cm)^2
U2=(1/2)(18.5)N/cm (s cm)^2
U1=U2
2 * (3.10cm)^2 = (s cm)^2
19.22 cm^2 = s^2* cm^2
s = +- sqrt(19.22)
s = +- 4.38cm