Consider the spring, mass and damper system depicted in Figure 3.35.

(a) Find the Input-Output model of the system.

(b) Find the Transfer Function model of the system and explain why it is called a second-order system.

(c) For the specific case where \(m=5 \mathrm{~kg}, k=10 \mathrm{~N} / \mathrm{m}\) and \(b=1 \mathrm{Ns} / \mathrm{m}\) :
(i) Find the specific Transfer Function model.
(ii) Find \(\zeta, \omega_{n}, M_{p}(\% O S), t_{s}, t_{p}\) and \(t_{r}\).

Transcribed Image Text:

k + x(t) b Figure 3.35 Spring, mass and damper system. m +f(t)