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Differential equation defining free damping vibration motion, It is given as m" (t) + ux' (t) + kx = 0. In the critical case where l=(u/ k), µ> O, 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 t =(2/1 - A /B)

Differential equation defining free damping vibration motion, It is given as m" (t) + ux' (t) + kx = 0. In the critical case where l=(u/ k), µ> O, 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 t =(2/1 - A /B)

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Differential equation defining free damping vibration motion , It is given as m" (t) + ux ' (t) + kx = 0. In the critical case where 1=(u/ k) , u> 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 t =(2/1 - A /B)
Transcribed Image Text:Differential equation defining free damping vibration motion , It is given as m" (t) + ux ' (t) + kx = 0. In the critical case where 1=(u/ k) , u> 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 t =(2/1 - A /B)
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