Question

A 35.0kg child swings on a playground swing 2.8m long. a) what is the period of her motion? b) If her older brother, who weighs twice as much as she does, rides the swing instead what is the period of the motion? (assume the center of mass to be at the postiion of the seat in both cases)

Answer 1

For a pendulum, angular frequency is

w=sqrt(g/l) where w is the angular frequency, g is the acceleration of gravity, and l is the length of the pendulum.

Once you find angular frequency (the measure of how fast the system travels through 1 radian), you need to find the frequency (the measure of how many cycles the system goes through in 1 second). Because there are 2pi radians in one cycle. f=w/2pi

Once you know frequency you can find period by simply inverting the frequency. (period just means how long it takes the system to go through one cycle)

For the second part, notice that mass is nowhere in these equations. So the period will be the same regardless of who is on the swing.