Question

Two parallel SHMs are given by `x_1 = 10 sin (8pit + pi/6) m and x_2 = 20 sin 8pit m` Find the resultant amplitude.

Answer 1

Comparing given equations with general equation of S.H.M 

x = a sin (ωt+ a) we get

`a_1 = 10 m, a_2 = 20 m, a_1 = pi/6, a_2 = 0`

Resultant amplitude,

`R = sqrt (a_1^2 + a_2^2 + 2a_1a_2 cos (a_1 - a_2)`

∴ `R = sqrt (10^2 + 20^2 + 2xx 10 xx 20 cos (pi/6))`

`= sqrt (100 + 400 + 400 xx sqrt3/2)`

`= sqrt (500 + 200 xx 1.732)`

`= sqrt (500 + 346.4)`

`= sqrt846.4`

∴ R = 29.09 ≈ 29.1