In assume that the differential equation of a simple pendulum of length L is Lθ" + gθ...

In assume that the differential equation of a simple pendulum of length L is Lθ" + gθ = 0, where g = GM/R2 is the gravitational acceleration at the location of the pendulum (at distance R from the center of the earth; M denotes the mass of the earth).

Two pendulums are of lengths L1 and L2 and—when located at the respective distances R1 and R2 from the center of the earth—have periods p1 and p2. Show that