- #1
Fascheue
Homework Statement
Find the amplitude of the motion given by x(t) = C cos ωt + D sin ωt.
Homework Equations
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x(t) = C cos ωt + D sin ωt
The Attempt at a Solution
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x(t) = C cos ωt + D sin ωt
x’(t) = -Cω sin ωt + Dω cos ωt
0 = -Cω sin ωt + Dω cos ωt
0 = -C sin ωt + D cos ωt
C sin ωt = D cos ωt
tan ωt = D/C
ωt = arctan D/C
t = (arctan D/C)/ω
x((arctan D/C)/ω) = C cos ω((arctan D/C)/ω)+ D sin ω((arctan D/C)/ω)
x((arctan D/C)/ω) = C/sqrt(1 + (D/C)^2) + D^2/Csqrt(1 + (D/C)^2)