For the mechanism in the posture shown, the constant angular velocity of input link 2 is 2

For the mechanism in the posture shown, the constant angular velocity of input link 2 is ω2 =

3kˆ rad/s. The free length of the linear spring attached between ground pin O1 and pin A is 20 in, and a viscous damper is attached between pin O and link 3. The torque acting on link 2 is T12 = −13.3kˆ in · lb, there is a horizontal force, P, acting at pin A, and gravity is in the negative y direction. The known data (where R2 is the vector from bearing O2 to mass center G3, and R3 is the vector from ground pin O to mass center, G3) are shown in Table P12.58.

Determine:

(a) the first-order kinematic coefficients of the spring and the damper,

(b) the potential energy of the spring,

(c) the equivalent mass moment of inertia, and

(d) the force P.