 Solution

ID: past-exam-of-the-physics-a-course-of-the-university-of-cambridge/2015/paper-2/section-b/b6/c/solution

For

b^{2} < 4 mk

, put

ω_{d} = ω_{0}^{2} - γ^{2}

. Complex-conjugate roots give the real solution

x (t) = e^{- γ t} [C cos (ω_{d} t) + D sin (ω_{d} t)] .

ω_{d}

persists within a decaying exponential envelope. damping reduces the oscillation frequency below

ω_{0}

. Constants in all three cases are determined by two initial conditions.

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