• Tags: pendulum, time-period, graph
• Difficulty: Foundation

T = 2pisqrt(L/g), so g = 4pi^2L/T^2. Effective length L = string length + radius of bob (distance from pivot to center of mass). Measure time for 20-50 complete oscillations to minimize timing error: T = total time/N. Plot T^2 vs L: a straight line through the origin with slope = 4pi^2/g, giving g = 4pi^2/slope. Sources of error: (1) Large amplitude (T increases for theta > 5 degrees — keep amplitude small). (2) Air resistance (use a dense, compact bob). (3) String not inextensible. (4) Parallax in measuring L. (5) Reaction time in stopwatch. Percentage error in g: Delta_g/g = Delta_L/L + 2Delta_T/T (since g = 4pi^2*L/T^2, the power of T is 2). This means timing errors affect g more than length errors.