In Problems 5 through 8, 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).

Most grandfather clocks have pendulums with adjustable lengths. One such clock loses 10 min per day when the length of its pendulum is 30 in. With what length pendulum will this clock keep perfect time?