Question

Question #7c91f

Answer 1

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)

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

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`