A point mass

Question

Displacement  of point mass X1=a sin wt

X2= asin (wt +2pi/3). Adding a third sinusoidal  displacement  x3 =Bsin (wt+Ø). Brings the mass to a complete  rest.

Then find the value of B andØ

Answer 1

according to the question particle will be at rest after adding these displacements

above equation will be zero if the coefficients of sinωt and cosωt will be zero so

but this value of ϕ does not satisfy the equations (1) and (2) so