2. How long must a simple pendulum be if it is to make exactly one swing per sev

Question

2.

How long must a simple pendulum be if it is to make exactly one swing per seven seconds? (That is, one complete oscillation takes exactly 14 s .) After landing on an unfamiliar planet, a space explorer constructs a simple pendulum of length 47.0cm . The explorer finds that the pendulum completes 91.0 full swing cycles in a time of 127s. What is the magnitude of the gravitational acceleration of this planet? Your grandfather clock's pendulum has a length of 0.9930 m.If the clock runs slow and loses 24s per day, how should you adjust the length of the pendulum? Enter positive value in case of increasing its length, otherwise enter negative value

Explanation / Answer

1) L = T^2 g/ (4 pi^2)

= 14^2 * 9.8 / (4 pi^2)

= 48.65 m

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2) T = 127 / 91

T = 2 pi sqrt(L/g)

g = 4 pi^2 L / T^2

= 4 pi^2 * 0.47 / (127 / 91)^2

g = 9.53 m/s2

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3) There are 3600 * 24 = 86400 seconds in a day.

24 / 86400 = 0.0002777

That means the period is off, and is 2s

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