(Period of oscillation of pendulum) Conservation of energ; dictates that the angular displ...

(Period of oscillation of pendulum) Conservation of energ; dictates that the angular displacement θ(t) of a pendulum, of length l and mass m, satisfies the differential equation

From show that

where T is the period and θ0 is the maximum swing. We expect T to depend on θ0 so we denote it asT(θ0). For the case θ0 = π/2, show that

NOTE: You may use results from the preceding exercises.