Please show all work. No guesses please! Consider the two \"gigantic\" simple pe

Question

Please show all work. No guesses please!

Consider the two "gigantic" simple pendulums with identical masses but with different lengths as shown below. Suppose they are released from rest from position A at the same time as shown. So you understand that they will not oscillate in harmony since they will have different periods of oscillation. But at a later time we will see both pendulums reaching the position A simultaneously. When will it take place? (calculate the time taken from the start). Take g= 980 cm/s2 . Must show all the calculations.

Explanation / Answer

L1 = 85.5 cm

g = 980 cm/s^2

Time period of 1 = 2*pi*(L1/g)^1/2

= 0.5907*pi = 1.856

L2 = 534.4 cm

Time period of 2 = 2*pi*(L2/g)^1/2

= 1.4768*pi = 4.64

Find the LCM of both

WE GET 9.28 s

It will take place when First pendulum comes at A For fifth time

It will take place when the Second pendulum comes at A for the second time.

SO THE TIME IS 9.28 seconds

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