Question

A particle is subjected to two SHMs simultaneously
`X_(1) = a_(1) sinomegat` and `X_(2) = a_(2)sin(omegat + phi)`
Where `a_(1) = 3.0 cm, a_(2) = 4.0 cm`
Find resultant amplitude if the phase difference `phi` has values (a) `0^(0)`, (b) `60^(0)`, (c) `90^(0)`

Answer 1

Correct Answer - (a) `7 cm` (b) `sqrt(37) cm = 6.1 cm` (c) `5 cm`
`A_(r) = sqrt(A_(1)^(2)+A_(2)^(3)+2A_(1)A_(2)costheta)`
(a) `A_(r) = sqrt(3^(2)+4^(2)+2xx3xx4xxcostheta) = 7 cm` (b) `A_(r) = sqrt(3^(2)+4^(2)+2xx3xx4xxcos60) = sqrt(37)cm = 6.1cm`
(c) `A_(r) = sqrt(3^(2)+4^(2)+2xx3xx4xxcos90) = 5 cm`