The time period of pendulum clock is given by
T = 2π\(\sqrt{\frac{l}{g}}\) , or T ∝ \(\sqrt l\)
During summer, length of the pendulum increase due to which the time period T increase and pendulum takes more time to complete one oscillation. Thus it slows in summer.
During winter length decrease, decreasing the time period. Consequently pendulum gains time and clock becomes fast.
