Question

Find the amplitude of the harmonic motion obtained by combining the motions
`x_(1) = (2.0 cm) sin omega t`
and `x_(2) = (2.0 cm) sin (omega t + pi//3)`.

Answer 1

The two equation given represent simple hormonic motion along the X-ray with amplitudes `A_(1) = 2.0 cm and A_(2) = 2.0 cm`. The phase different between the two simple harmonic motion is `pi//3`. The resultant simple harmonic motion will have an amplitude A gives by
`A = sqrt(A_(1)^(2) + A_(2)^(2) + 2 A_(1)A_(2) cos delta)`
`= sqrt((2.0 cm)^(2) (2.0 cm)^(2) + 2 (2.0cm)^(2) cos ((pi)/(3))) = 3.5 cm`