Question

We measure the period of Oscillation of a simple pendulum. In successive measurements the readings turn out to be 2.63s, 2.56s, 2.42s, 2.71s, 2.80s. Calculate the absolute error, Relative error and Percentage error?​

Answer 1

Explanation:

Arithmetic mean,a mean = 2.63+2.56+2.42+2.71+2.80/5

= 13.12 / 5

a mean = 2.624 s

Absolute error,

delta a1 = 2.63 - 2.62

= 0.01 s

delta a2 = 2.56 - 2.62

= 0.06 s

delta a3 = 2.42 - 2.62

=0.20 s

delta a4 2.71 - 2.62

= 0.09 s

delta a5 = 2.80 - 2.62

= 0.18 s

delta a mean =ldelta a1l+ldelta a2l+ldelta= 0.09 s delta a5 = 2.80 - 2.62 = 0.18 s

delta a mean =ldelta a1l+ldelta a2l+ldelta a3+ldelta a4l+ldelta a51/5

= 0.108

= 0.11 s

a = a mean (+/-) delta a mean =2.51 < 2.62 < 2.73

= 2.62 (+/-) 0.11

Relative error=0.11, 2.6

= 0.04 s

Percentage error = delta a mean / a mean

x 100

= 0.11 / 2.6 x 100

= 4%

Answer 2

Answer:0.11s

Explanation:T=  

5

2.63+2.56+2.42+2.71+2.80

​

 

5

13.12

​

=2.624=2.62

2.62−2.63=−0.01

2.62−2.56=+0.06

2.62−2.42=+0.20

2.62−2.71=−0.09

2.62−2.80=−0.18

Average absolute error  

5

0.01+0.06+0.20+0.09+0.18

​

 

0.545=0.108=0.11s