Answer:
Explanation:
y(t) = Acos(ωt)
taking log on both the sides
lny = lnA + lncos(ωt)
differentiating on both sides
[tex]\frac{dy}{y} = \frac{dA}{A} +sin\omega t\frac{d\omega t}{cos\omega t}[/tex]
% change in y = % change in A + sinωt.% change in ωt
% change in A = [tex]\frac{2}{23} \times 100[/tex] = 8.7 %
% change in ωt = % change in ω + percentage change in t
= % change in ω = [tex]\frac{1}{.40}[/tex] %
= 2.5 %
percentage change in t = [tex]\frac{ .001 }{ .05 }\times 100[/tex]
= 2 %
% change in y = 8.7 % + 2.5 % + 2 %
= 13.2 %
y = Acos(ωt
= 23 cos [tex]\frac{2\pi}{.4}\times.05[/tex]
= 23 x cos 45
=16.25 mm
change in y = 13.2 % of 16.25
= 2.14 .
