A certain vibrating system satisfies the equation u′′ + γu′ + u = 0. find the value of the damping coefficient γ for which the quasi period of the damped motion is 50% greater than the period of the corresponding undamped motion.

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Mathematics

Sarahi Mccormick

30 August, 05:30

A certain vibrating system satisfies the equation u′′ + γu′ + u = 0. find the value of the damping coefficient γ for which the quasi period of the damped motion is 50% greater than the period of the corresponding undamped motion.

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Barton · Answer 1

The characteristic equation for this is r^2 + yr + 1 = 0. Its roots are r = y/2 + / - isqrt (1-y^2/4). Finding the general solution to this equation gives us y = sqrt (20/9), which is the value of the damping coefficient y for which the quasi period of the damped motion is 50% greater.