I'm supposed to derive a relationship in which the change in gravity δg\delta g is linked to the change in length of the spring δs\delta s . When the beam is tilted due to increased weight or gravity, the extra weight will tilt, and this will enhance the rotation. I understand this so far, but I can't figure out how to connect these two system. Without the extra mass one could easily used the Hooke's law ΔF=mδg=κδs\Delta F=m\delta g=\kappa \delta s . I can't figure out how to fit the extra weight in this. For an inverted pendulum τ=mglsin⁡θ\tau=mgl\sin\theta . How do I relate this with the Hooke's law? Or am I wrong from the beginning? In a stable system without the extra weight, should I still consider not only Hooke's law but also the torque?