Do #31 where the resources it references are found below. Show all work. From Or

Question

Do #31 where the resources it references are found below. Show all work. From Ordinary Differential Equations by Tenenbaum and Pollard.

31. By integrating (28.78), remember the initial condition is t 0, 00, show that du (28.79) t(0) eo COS u cos Bo Since at t 0, 0 60, w 0, one-half of a period elapses when 0 --0o. Use this fact, (28.79), and the fact that cos u is an even function, i.e., cos (-u) cos u, to show that the period T of the pendulum is given by (28.791) 2g J-oo Mcos u --cos 00 0 1 cos u cos 6o For definition of moment of inertia, Bee Lesson 30M-B.

Explanation / Answer

Solution:-

Given

Clock with pendulum of sufficient length = l

Period = 2 second

Amplitude = 4 degree

In each 2 second the clock is incorrect by 0.00061 sec

We have to find the error in the clock at the each 24 hour.

Since it is given that in each 2 second the clock is incorrect by 0.00061 sec

Hence in each one second the correct is incorrect by = 0.00061/2 = 0.000305 sec

Since we have to find error in clock ar each hour, hence we have to find error in 24*3600 seconds

= 0.000305*24*3600 = 26 seconds slow approximately

Hence the error in clock at the end of each 24 hours = 26 seconds.

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