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1. The swing angle of the pendulum is \"small\" when the period following from t

ID: 1407902 • Letter: 1

Question

1. The swing angle of the pendulum is "small" when the period following from the full analysis (Eq.(2) in the text) differs from the period obtained using the truncated formula, Eq.(1) at most by 0.5%. If we consider the summation in Eq.(2) only up to the second term, calculate this angle in radians, and convert it to arc degrees.

2. In the experiment you will investigate a 1 meter long pendulum and a 0.1 meter long pendulum. How many seconds is the difference between the periods of these two pendulums based on the theory (Eq. (1)).

Eq.1 & Eq.2 are found in the reading below.

THANKS!

Explanation / Answer

a)

Eq1:

T= const. * (L/g)^1/2

Eq2:

T= [ (2pi)* (square root of (L/g)) ] * [ 1 + ((1/2)^2) * (sin^2 theta/2)+ ((1*3/2*4)^2)(sin^4 theta/2)+.....]

const. * (L/g)^1/2 = [ (2pi)* (square root of (L/g)) ] * [ 1 + ((1/2)^2) * (sin^2 theta/2)]

((1/2)^2) * (sin^2 theta/2) 0.005

theta 17º

Please post second question separately.