So we know that SHM can be described as:(adsbygoogle = window.adsbygoogle || []).push({});

x(t) = Acos(ωt + ϕ)

v(t) = -Aω sin(ωt + ϕ)

a(t) = -Aω^2 cos(ωt + ϕ)

it can be easily said that the max acceleration (in terms of magnitude) a SHM system can achieve is Aω^2

In Damped Harmonic Motion we know that:

x(t) = (A)(e^(-bt/2m))cos(ωt + ϕ)

given that:

A' = (A)(e^(-bt/2m))

ω' = sqrt( (ω^2) - (b/2m)^2 )

Is it true that the max acceleration at any given time is (A')(ω')^2?

My intuition tells me that the above statement is not true =/

because differentiating the function x(t) = (A)(e^(-bt/2m))cos(ωt + ϕ) gives me a complex function (which has sine & cosine in it) & it doesn't really give me anything close to the (A')(ω')^2 term

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# Queries on Damped Harmonic Motion

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