Question: The period, T, of oscillation in seconds of a pendulum clock is given by T = 2π√(l/g) where g is the acceleration due to gravity. The length of the pendulum, l, depends on the temperature, t, according to the formula l = l0(1 + α(t - t0)) where l0 is the length of the pendulum at temperature t0 and α is a constant which characterizes the clock. The clock is set to the correct period at the temperature t0. How many seconds a day does the clock gain or lose when the temperature is t0 + Δt? Show that this gain or loss is independent of l0.