The period of oscillation of a simple pendulum turns out to be 2.63 s, 2.56s, 2.42s, 2.71s, and 2.80s. Find :

a) True period of oscillation

b) Absolute error in each measurement

c) Mean absolute error

d) Fractional error

e) percentage error

f) Period of pendulum without error limits

hii

 

fr this u have to find mean value of the time period first

 = 2.63 + 2.56 + 2.42 + 2.71 + 2.80 / 5 = 2.624

 

2) Absolute error....

taking 2.624 as the true value of the tym period...

 

#T₁ = 2.62 - 2.63 = - 0.01

 

#T₂ = 2.62 - 2.56 = 0.06

 

#T₃ = 2.42 - 2.62 = 0.20

 

#T₄ = 2.62 - 2.71 = -0.09

 

#T₅ = 2.62 - 2.80 = - 0.18

 

so

 

#T = -0.01 + 0.06 + 0.20 - 0.09 - 0.18 / 5 = -0.02/5 = -0.004

 

Fractional error = #T / T = - 0.004 / 2.62 = 0.0015

 

 

%age error = -0.0015 x 100 = 0.15%