a mass spring damping system is shown in figure q4 equation q4 below d

Question

A mass-spring-damping system is shown in Figure Q4.
Equation (Q4) below describes the input (f(t)) and output (x(t)) function obtained from Newton's law: f(t)=m \frac{d^{2} x}{d t^{2}}+d \frac{d x}{d t}+k \cdot x(t) where k = 1kN/m, d = 20N s/m, m= kg (a) With the given input/output and Equation (Q4), calculate the transfer function.Denote this transfer function as G(s). (b) Calculate the poles of this system and assess its stability. (c) Calculate the impulse response of this system. Show details of your calculation. (d) Calculate the step response for the sampling points given in Table Q4. Show details of calculation.