Question

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

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`

Phase of SHM is given by

`δ = tan^-1 [(a_1 sin a_1 + a_2 sin a_2)/(a_1 cos a_1 + a_2 cos a_2)]`

`= tan^-1 [(10 sin (pi/6) + a_2 sin0)/ (10 cos (pi/6) + a_2 cos 0)]`

`= tan^-1 [(10xx 1/2 + 20 xx 0)/(10 xx sqrt3 /2 + 20 xx1)]`

`= tan^-1 [5/(5 sqrt3 + 20)]`

∴ `delta = tan^-1 [5/28.66]`

∴ `delta = tan^-1 (0.1745) = 9°54`'