(a) Given the differential equation [frac{d^{2} x}{d t^{2}}+7 frac{d x}{d t}+5 x=8 u(t) quad t geq 0]...
Question:
(a) Given the differential equation
\[\frac{d^{2} x}{d t^{2}}+7 \frac{d x}{d t}+5 x=8 u(t) \quad t \geq 0\]
Using MATLAB program, find
(i) $x(t)$ when all the initial conditions are zero
(ii) $x(t)$ when $x(0)=1$ and $\dot{x}(0)=3$.
(b) Given the differential equation
\[\frac{d^{2} x}{d t^{2}}+12 \frac{d x}{d t}+15 x=35 \quad t \geq 0\]
Using MATLAB program, find
(i) $x(t)$ when all the initial conditions are zero
(ii) $x(t)$ when $x(0)=0$ and $\dot{x}(0)=1$.
(iii) For the following differential equation, use MATLAB to find $x(t)$ when $x(t)$ when $x(0)=-1$ and $\dot{x}(0)=1$
\[\frac{d^{2} x}{d t^{2}}+8 \frac{d x}{d t}-4 x=18 u(t)\]
(c) For the following differential equation, use MATLAB to find $x(t)$ when $x(t)$ when $x(0)=-1$ and $\dot{x}(0)=1$
\[\frac{d^{2} x}{d t^{2}}+15 \frac{d x}{d t}+8 x=-9 u(t)\]
(d) For the following differential equation, use MATLAB to find $x(t)$ when $x(t)$ when $x(0)=-1$ and $\dot{x}(0)=1$
\[\frac{d^{2} x}{d t^{2}}+19 \frac{d x}{d t}+9 x=-3 u(t)\]
Step by Step Answer:
Analysis And Design Of Control System Using MATLAB
ISBN: 9788122424096
2nd Edition
Authors: R.V. Dukkipati