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x(1) = 3 sin omega t implies x(2) = 4 ...

`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.

Text Solution

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First write all `SHM's` in terms of sine functions with positive amplitude. Keep `"omegat"` withh positive sign.
`:. x_(1) = 3 sinomegat`
`x_(2) = 4 sin (omegat + pi//2)`
`A = sqrt(3^(2) + 4^(2) + 2 xx 3 xx 4cos'(pi)/(2)) = sqrt(9 + 16) = sqrt(25) = 5`
`tan phi = (4sin'(pi)/(2))/(3 + 4cos'(pi)/(2)) = (4)/(3), phi = 53^(@)` equation `x = 5 sin (omegat + 53^(@))`
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