Reference no: EM132205263

Assignment - Physical System Modeling, Time Response and Stability

For a mass-spring-damper mechanical system shown below,

1. Find the differential equations relating input force f(t) and output displacement x₁(t) and x₂(t) in the system.

(Hint: K, f_v and M are spring constant, friction coefficient and mass respectively).

2. Determine the transfer function G(s) = X₁(s)/F(s).

For the following questions, suppose

G(s) = 3 x (s+1.3/(s+1.4)(s²+2s+1.49))

3. Determine the system impulse response in the time domain.

4. Draw its root locus and comment on system stability.

5. If the system can be simplified using the system dominant pole technique into G₁(s) below, obtain the system response for a unit step input, and estimate the overshoot and settling time.

G₁(s) = (3x(0+1.3)/(0+1.4)(s²+2s+1.49)) = 3.9/(1.4(s²+2s+1.49))