Pendulum laboratory and resonance

Aim: to find g from the period of a pendulum. From T = 2π√(l/g) we get g = 4π²l/T², with T = t/N. Equipment: a ball on a string attached to a stand, a measuring tape, a stopwatch. The length l is the string length plus the radius of the ball (it is measured from the suspension point to the centre of the ball). The ball is deflected by no more than 6–8°, the time of N = 20, 30, 40 oscillations is measured, g is calculated each time, then g(mean) = (g₁ + g₂ + g₃)/3 and the error Δg = |g – g(mean)| are found. Sources of error: delay in starting and stopping the stopwatch, imprecise length measurement, breaking the small-oscillation condition. With more oscillations the relative error of the period is smaller. Work under the teacher’s supervision and fix the stand so that it cannot tip over.