Question

A performer seated on a trapeze is swinging back and forth with a period of 8.46 s. If she stands up, thus raising the center of mass of the trapeze + performer system by 33.9 cm, what will be the new period of the system? Treat trapeze + performer as a simple pendulum.

Answer 1

Here, as we know the time peroid (T) for simple pendulum is equlas to

T = 2 * Pi * sqrt (L/g).........(1)

Where L = length and g = 9.8

Now in the first case, we have time period but the value of length is not given. so using eq 1

L = T^2 * g /(4*Pi^2)

L= 8.46^2 * 9.8 / 4*3.14*3.14

L = 17.7 m

Now as given in question Trapeze + performer length = 33.9 cm or 0.339 m

The new length L2 = 17.78 - 0.339 = 17.44m

Now new time period(T2) is

T2 = 2*3.14*sqrt(17.44/9.8)

T2 = 8.37 sec

The new peroid of the system is 8.37sec