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

T = 2pisqrt$\frac{L}{g}$, so g = 4*$pi^2$L/$T^2$. 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 = 4$pi^2$/g, giving g = 4*$pi^2$/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 = $\frac{Delta_L}{L}$ + 2*$Delta_T$/T (since g = 4*$pi^2$*L/$T^2$, the power of T is 2). This means timing errors affect g more than length errors.