Question

By means of plotting find the amplitude of the oscillation resulting from the addition of the following three oscillations of the same direction:
`xi_(1) = a cos omegat, xi_(2) = 2a sin omegat, xi_(3) = 1.5 a cos (omegat + pi//3)`.

Answer 1

It is easier to do it analytically.
`xi_(1) = a cos omegat, xi_(2) = 2a sin omegat`
`xi_(3) = (3)/(2)a (cos .(pi)/(3) cos omegat - sin .(pi)/(3) sin omegat)`
Resultant vibration is
`xi = (7a)/(4) cos omegat + a(2-(3sqrt(3))/(4)) sin omegat`
This has an amplitude `= (a)/(4) sqrt(49 xx (8 - 3 sqrt(3))^(2)) = 1.89 a`