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LameGeek
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So we know that SHM can be described as:
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
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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