(Solved): 3.1. Use the Routh-Hurwitz method of determinants to investigate the stability of a system characte ...

3.1. Use the Routh-Hurwitz method of determinants to investigate the stability of a system characterised by the transfer function $G(p)=\frac{p?1}{3p^4+6p^3+2p^2?3p+4}$ 3.2. A system with input $u(t)$ and output $x(t)$ is described by the differential equation $x^{???}+3x^{??}+4x^{?}+2x=u^{?}?2u$ Use Laplace transforms to determine the impulse response of the system and discuss the progress of the response as $t??$ and comment about the stability of (11) the system Question Four [12] 4. The sag of a horizontal beam of length $10\mathrm{m}$ is described by the differential equation $\frac{d^{4}y}{d{x}^4}=\frac{kH(x?5)}{50000},k?\mathbb{R},y(0)=y^{?}(0)=0,y^{??}(0)=\frac{3}{4000},y^{???}(0)=?\frac{1}{10000}$ 4.1. Use Laplace transforms to determine the deflection equation for the beam (8) 4.2. Compute the sag when $x=8m,k=?1000$, discuss the results and then determine the bending moment when $x=7\mathrm{m}$ and $k=1$