A particle is subjected to two `SHMs x_(1) = A_(1) sin omegat` and `x_(2) = A_(2)sin (omegat +(pi)/(4))`. The resultant `SHM` will have an amplitude of
A
`(A_(1)+A_(2))/(2)`
B
`sqrt(A_(1)^(2)+A_(2)^(2))`
C
`sqrt(A_(1)^(2)+A_(2)^(2)+sqrt(2)A_(1)A_(2))`
D
`A_(1)A_(2)`
Text Solution
Verified by Experts
The correct Answer is:
C
`A = sqrt(A_(1)^(2)+A_(2)^(2)+2A_(1)A_(2)cosphi)`
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Knowledge Check
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A
`2A cos (phi)/4`
B
`Asqrt(2cosphi//2)`
C
`2A (phi)/2`
D
`Asqrt(2(1+cos(phi)/4))`
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