Q.In summer season, a pendulum clock is regulated as a second's pendulum and it keeps correct time. During winter, the length of the pendulum decreases by 1%. How much will the clock gain or lose in one day? (g = 9.8 m/s²)

A simple pendulum is a heavy bob suspended by a light, inextensible string from a rigid support. For small angular displacements theta (below about 10 degrees), the restoring force on the bob, F = -mgsin(theta), can be approximated (using sin(theta) is approximately theta, and theta is approximately x/L, where x is the arc-length displacement and L the string length) as F = -(mg/L)x -- directly proportional to displacement and oppositely directed, exactly the S.H.M. condition. This gives the acceleration-per-unit-displacement as g/L, and hence the period T = 2pisqrt(L/g), derived under three assumptions: small amplitude, a long string, and motion confined to a single vertical plane. The corresponding "laws of the simple pendulum": period is proportional to sqrt(L), inversely proportional to sqrt(g), independent of the bob's mass, and independent of amplitude (for small amplitude). …