If possible please show how to achieve answers using excel. If not possible plea

Question

If possible please show how to achieve answers using excel. If not possible please show ;method used to achieve answer.

One of the classic methods for measuring the acceleration due to gravity to to use a simple pendulum. One measures the period, T, of the oscillations of the pendulum, which consists of mass, m, suspended from a cable of length . Tf the oscillations are small less than a few degrees then the period of oscillation is given by: T = 2 v g Suppose that you hang a cat with a mass of 3.94 +/ 0.38 kg from a cable whose length is measured to be 9.62 0.03 m. The experiment is performed, and you measure the time for 100 oscillations of the pendulum. The TOTAL time for these 100 oscillations is measured to be 626.2 0.2 s. (a) What is the average value for the period of oscillation of the pendulum? (b) What is the uncertainty in the average value of the period of oscillation of the pendulum? (c) What is the average value of the acceleration due to gravity, as measured in this experiment? (d) Assuming that the uncertainties quoted above follow a uniform error distribution, what is the measured uncertainty in the acceleration due to gravity? (e) Assuming that the uncertainties quoted above follow a Gaussian error distribution, what is the measured uncertainty in the acceleration due to gravity? m/s 2 m/s 2 m/s 2

Explanation / Answer

(a) Average value for the period of oscillation of the pendulum = 626.2/100 = 6.262 seconds

(b) Uncertainty in the average value of the period of oscillation of the pendulum. = 0.2/100 = 0.002 seconds

(c) average of the value acceleration due to gravity

g = 42 l/T2 = 4 * * * 9.62/ (6.262)2 = 9.6852 m/ sec2

(D) Uncertainly in acceleration  g/g =  l/l + 2 T/T = 0.03/9.62 + 2 * 0.002/ 6.262 = 0.00375

g = 9.6852 * 0.00375 = 0.0634 m/sec2

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