ax" + bæ' + cx = f(t), x(0) = 0, x'(0) = 0, for time 0 0. Find X(s) = L {æ(t)} and F(s) = L{f(t)}. X(s) = help (formulas) F(s) = help (formulas) Now find the system transfer function, H(s). H(s) help (formulas) What will be the output if a Heaviside unit step input f(t) = u(t) is applied to the system? New x(t) help (formulas)

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.