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What is the amplitude of the S.H.M. obta...

What is the amplitude of the S.H.M. obtained by combining the motions.
`x_(1)=4 "sin" omega t cm, " " x_(2)=4 "sin"(omega t + (pi)/(3)) cm`

A

8 cm

B

`4sqrt(3) cm`

C

6 cm

D

`2 sqrt(3) cm`

Text Solution

Verified by Experts

The correct Answer is:
B
`A_(1)=4cm, A_(2)=4 cm and phi =(pi)/(3)`
`therefore` The resul"tan"t amplitude
`=sqrt(A_(1)^(2)+A_(2)^(2)+2A_(1)A_(2) "cos" phi)`
`=sqrt(4^(2)+4^(2)+2xx4xx4xx "cos" 60^(@))`
`=sqrt(16+16+16)=sqrt(48)=4sqrt(3) cm`
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