If $$a$$ and $$b$$ are constants, the most general solution of the differential equation $$\,{{{d^2}x} \over {d{t^2}}} + 2{{dx} \over {dt}} + x = 0$$ is

The unilateral Laplace transform of $$f(t)$$ is $${1 \over {{s^2} + s + 1}}$$. Which one of the following is the unilateral Laplace transform of $$g\left( t \right) = t.f\left( t \right)?$$

An 8085 microprocessor executes “STA 1234H” with starting address location 1FFEH (STA copies the contents of the Accumulator to the 16-bit address location). While the instruction is fetched and executed, the sequence of values written at the address pins $${A_{15}}$$ − $${A_{8}}$$ is

The steady state output of the circuit shown in the figure is given by $$$y\left( t \right) = {\rm A}\left( \omega \right)\sin \left( {\omega t + \phi \left( \omega \right)} \right)$$$

If the amplitude $$\left| {{\rm A}\left( \omega \right)} \right| = 0.25$$, then the frequency $$\omega $$ is