A single input single output system with $$y$$ as output and $$u$$ as input, is described by $$${{{d^2}y} \over {d{t^2}}} + 2{{dy} \over {dt}} + 10y = 5{{d\,u} \over {dt}} - 3\,u$$$
For the above system find an input $$u(t),$$ with zero initial condition, that produces the same output as with no input and with the initial conditions.
$${{d\,y\left( {{0^ - }} \right)} \over {dt}} = - 4,\,\,\,y\left( {{0^ - }} \right) = 1$$

A first order system is initially at rest and excited by a step input at time $$t=0.$$ Its output becomes $$1.1$$ $$V$$ is in $$4$$ seconds and eventually reaches a steady state value of $$2V$$. Determine its time

The impulse response of a network is $$h\left( t \right) = 1$$ for $$0 \le t < 1$$ and zero otherwise. Sketch the impulse response of two such networks in cascade, neglecting loading effects.