1.6 Exercise 54

A pendulum is made of a rod of length L and negligible mass, but capable of thermal expansion, and a weight of negligible size. (a) Show that when the temperature increases by dT, the period of the pendulum increases by a fraction $\alpha d T / 2$. (b) A clock controlled by a brass pendulum keeps time correctly at $10 ° \text{C}$. If the room temperature is $30 ° \text{C}$, does the clock run faster or slower? What is its error in seconds per day?