Differential equation defining free damping vibration motion , It is given as m" (t) + ux ' (t) + kx = 0 . In the critical case where 2=(µl k) , µ> 0, where the roots of the characteristic equation are equal to 0^+, the solution of the equation is x(t)=(A+Bt)e^(-at /2). Show that for AA <2B, X(t) initially increases and reaches its maximum at the value %3D t =(2/2 - A /B)

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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.