The period T of a simple pendulum is given by where L is the length of the pendulum and g is the acceleration due to gravity.
a. Assume g = 9.80 m/s2 exactly, and that L= 0.742 ± 0.005 m. Estimate T, and find the uncertainty in the estimate.
b. Assume L = 0.742 m exactly, and that T = 1.73 ± 0.01 s. Estimate g, and find the uncertainty in the estimate.
Step1 of 3:
Let T be the period of of a simple pendulum and it is given by
L = length of the pendulum
g = acceleration due to gravity
Here our goal is:
a).We need to Estimate T, and find the uncertainty in the estimate by Assuming g = 9.80 exactly, and that L = 0.7420.005m
b).We need to Estimate g, and find the uncertainty in the estimate by Assuming L = 0.742 m exactly, and that T = 1.730.01 s.
Step2 of 3:
From the given information we have g = 9.80, L = 0.742,
mathematical constant and its value is 3.14
Differentiate above equation with respect to “L” we get
Let u = L/g
du = 1/g
Apply chain rule to above equation to get a differential equation and it is given by
Substitute “u” value in above equation we get
Hence, = 1.1645.
The estimate of uncertainty is given by