In a contraption built by a fraternity, a person sits at the center of a swinging platform...

In a contraption built by a fraternity, a person sits at the center of a swinging platform with weight Wp = 800 lb and length L = 12 ft suspended via two identical arms each of length H = 10 ft and weight Wa = 200 lb. The platform, which is at rest when θ = 0, is put in motion by a motor that pumps the ride by exerting a constant moment M in the direction shown whenever 0 ≤ θ ≤ θp while exerting zero moment for any other value of θ.

Figure P8.27

Neglecting the mass of the person, neglecting friction, and letting θp, = 20°, determine the value of M required to achieve a maximum value of θ equal to 90° in 6 full swings. Model the arms AB and CD as uniform thin bars.