Question

3. A motor with torque T and inertia Jm drives a load of inertia Joad via a shaft which may be assumed to have infinite stiffness and viscous damping b. Determine the transfer function between the torque T and the shaft speed w. 4. Find the transfer function X2(s)/F (s) of the spring-mass system shown in Figure 4. The system moves over a frictionless surface X2 X1 b k2 k1 M2 M1 Figure 4. A 2 DOF spring-mass system over a frictionless surface.

Answer 1

3. Since the rod has infinite stiffness, it implies that both the inertia components will be rotating the same angle. Hence this is actually a one degree of freedom system. Therefore one differential equation will be there to explain the system. Since both are rotating same angle we can add up the inertia's and get the differential equation as,

(Jm + Jond)6 — Т — бӧ

Joad )w = T _ bw (Jm

Taking Laplace Transform we get,

(JmJoad) Sw(s) = T(s) - bw(s

Е (m + Joud)s + b)w(s) — Т(s)

Therefore we can write the transfer function as,

w(s) T(s) (JmJioad)s +b