In a grandfather clock, the constant period of a pendulum is utilized to keep ti

Question

In a grandfather clock, the constant period of a pendulum is utilized to keep time. While this is a good method for keeping time, it is not perfect, as the period is affected by the length of the pendulum, the gravity under which it is placed, and the maximum angle. You are going to investigate these as in a pendulum. This is a theoretical physics experiment. We derived the period of a pendulum, T, in class using the small angle approximation. sin? ?, which is true for angles less than about 10.. The accurate equation is much more complex ?=-bl1+G)'sin2?+(H)'s n.?+(?//)2sin ?+..1 2 2.4.6 The first order approximation uses only the first term in the above equation, hence we see T2 s the first order approximation. The second order approximation uses the first two terms, and so on. 1. Suppose you wanted to make a pendulum for a clock, and you wanted to have the period be exactly 2 seconds (tick-tock). What length should the pendulum be? Use the first order approximation and use g 9.8 m/s. Write your answer out to 8 decimal places

Explanation / Answer

Time period for first order assumption :

T = 2?(L/g)0.5

Given that T = 2 sec ,g = 9.8

2 = 2?(L/9.8)0.5

L/9.8 = 0.101321184

L = 0.101321184*9.8

L = 0.992947599 m

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