A hollow sphere of mass M and radius R is hit by a pendulum of
mass m and length L that is raised at an angle θ. After the
collision the pendulum comes to a stop and the sphere rolls forward
into a spring with stiffness k on an incline of ϕ. Find an
expression for how far ∆x the spring compresses along the incline.
Use only m, L, M, R, θ, ϕ, k and appropriate constants.