The two particles performing S.H.M. have a phase difference of `pi`. If the amplitude of second particle is three times the amplitude of first particle, then the amplitude of resultant motion will be

Options

A. equal to initial
B. three times initial
C. twice the initial
D. half of the initial

Answer

C

Explanation

`R=sqrt(A_(1)^(2)+A_(2)^(2)+2A_(1)A_(2)cos(prop_(1)-prop_(2)))`
`=sqrt(A^(2)+9A^(2)-6A^(2))`
`R=sqrt(4A^(2))=2A`