Question #7c91f

1 Answer
David Y.
May 16, 2015

My guess would be #T^2= (4pi^2)/g *((L_1 + L_2)/2)#
By obstructed I am assuming the pendulum bob is on a string that hits a peg or other obstruction at the halfway point of its swing (see diagram)

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I'm not 100% sure but believe the period of this type of pendulum will be the average of the period on the unobstructed side #"Length"_1# and the obstructed side #"Length"_2#

The relationship between period and length is given as

enter image source here

So for #T^2# the relationship would be

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

The mean value of the two periods (and the period of the obstructed pendulum) would be equal to

#((4pi^2L_1)/g + (4pi^2L_2)/g)/2or (4pi^2)/g *((L_1 + L_2))/2 #

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