Example 5 A S.H.M. is given by x = 5 sin (3t + f) is to be split into two components such that one leads it by 30^{0} and the other lags it by 80^{0}. Find the components.
Solution
Let the required components be given by x_{1} = a_{1}sin ( 3t + f  80^{0}) and x_{2} = a_{2} sin (3t + f +
30^{0}). We can solve the equation graphically as shown in the figure.
Procedure
Example 6 A body is subjected to two S.H.M. as given below
x_{1} = 15 sin (wt + p/6) and
x_{2} = 8 cos (wt + p/3) what harmonic motion, should be given to the body to bring it to 'static equilibrium'?
Solution
