Initial Conditions

The relation between the input current (I) and the output voltage (V) of a circuit is governed by the equation: $C \frac{dV}{dt} = I(t) - m(t)$. The circuit is excited by $I(t) = q...

The input $$-3\mathrm e^{2\mathrm t}\;\mathrm u\left(\mathrm t\right)$$, where u(t) is the unit step function, is applied to a system with transfer function $$\frac{s-2}{s+3}$$. If...

The input $$ - 3{e^{2t}}\,\,u\left( t \right)$$, where u(t) is the unit step function$$\, {{s - 2} \over {s + 3}}$$. If the initial value of the output is -2, then the value of the...

The state equation of a second-order linear system is given by $$\mathop x\limits^ \bullet \left( t \right) = Ax\left( t \right),x\left( 0 \right) = {x_0}.$$ For $${x_0} = \left[ {...

Consider the differential equation $${{{d^2}y\left( t \right)} \over {d{t^2}}} + 2{{dy\left( t \right)} \over {dt}} + y\left( t \right) = \delta \left( t \right)$$ with $$y\left( t...

A certain linear time invariant system has the state and the output equations given below $$$\left[ {\matrix{ {\mathop {{x_1}}\limits^ \bullet } \cr {\mathop {{x_2}}\limits^ \bulle...

The transfer function of a linear system is the

The transfer function of a linear system is the