Solved: Consider a harmonic oscillator with mass m = 1,

Chapter , Problem 35

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Consider a harmonic oscillator with mass m = 1, spring constant k = 3, and a (fixed) damping coefficient b. Then the motion of the oscillator is modeled by the equation d2 y dt2 + b dy dt + 3y = 0. What is the quickest rate at which a solution can approach the equilibrium state? (The equilibrium state is the point (y, v) = (0, 0) where v = dy/dt. Your answer should depend on the value of b.)

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