The segmented “dummy” of Prob. 6/103 is repeated here. The hip joint O is assumed to rem...

The segmented “dummy” of Prob. 6/103 is repeated here. The hip joint O is assumed to remain fixed to the car, and the torso above the hip is treated as a rigid body of mass m. The center of mass of the torso is at G and the radius of gyration of the torso about O is k₀. Assume that muscular response acts as an internal torsional spring which exerts a moment on the upper torso, where K is the torsional spring constant and θ is the angular deflection from the initial vertical position. If the car is brought to a sudden stop with a constant deceleration a, derive the differential equation for the motion of the torso prior to its impact with the dashboard.