Since the springs are in parallel, they will both have the same displacement. Knowing this and examining the equation for the restoring force of the spring you can find that:
F = kx
F = k1x + k2x = (k1+k2)x
Keeping the second equation in the same "form" as the first,
k = k1 + k2...
Homework Statement
I included the problem as an attachment. My difficulty lies within understanding how to account for the applied torque within the Lagrangian and subsequent Euler-Lagrange equations, which is what I want to use to determine the equations of motion of the bead on the hoop...