Question

Please, work at least one of the problems completely, so I can know how to work it out.

This is the formula: T=2π√(L/g)

Table of Data
To investigate period dependence on length

Mass, m: pick any mass. Record here. 0.005 Ib = 2.267962 grams
Angle, θ = 20 degrees or less.

Suggested Lengths (m)	Total time of 5 cycles	Experimental Period (Divide total time by 5)	Theoretical Period (Use Eq. (1))	%Err
1.20	9.60	1.92
1.00	7.63	1.526
0.90	7.56	1.512
0.50	6.40	1.28
0.40	6.19	1.238

Answer 1

The period T of a simple pendulum (measured in seconds) is given by the formula:

T=2 π √ (L/g)

g = 4π²L/T²

g₁ = 12.85 m/s² (experimental values taken as L = 1.20 and T = 1.92);

g2 = 16.95 m/s² (experimental values taken as L = 1.20 and T = 1.92);

similarly, g3 = 15.54 m/s² , g4 = 12.04 m/s², g5 = 10.3 m/s²

Avarage g = 13.5 m/s²

Theoretical Period: for length 1.20 m ;   Experimental Period : for length 1.20 is 1.92 s;

T=2π√(L/g) = 2π√(1.20/13.5) = 1.87 s;

% error = (Experimental Period - Theoretical Period)/(Theoretical Period) *100

   = (1.92 - 1.87)/1.87*100

= 2.67%.