`x_(1) = 3 sin omega t implies x_(2) = 4 cos omega t`. Find (i) amplitude of resultant SHm, (ii) equation of the resultant SHm.

Explanation

First , write all SHMs in term of sine function with positive amplitude. Keep `omega t` with positive sign.
`x_(1) = 3 sin omega t, x_(2) = 4 sin (omega t + pi//2)`
`A = sqrt(3^(2) + 4^(2) + 2 xx 3 xx 4 cos) (pi)/(2) = sqrt (9 + 16) = sqrt(25) = 5` `= sqrt (9 + 16) = sqrt(25) = 5`
`tan phi = (4 sin (pi)/(2))/(3 + 4 cos (pi)/(2))= (4)/(3). phi = 53^(@)`
Resultant equation, `x = 5 sin (mega t + 53^(@))`