Question

If two simple harmonic motions are given as
`x_(1)=Asin omegat andx_(2)=(A//2)sinomegat+(A//2)cosomegat`, then the ratio of their amplitudes is
A. 1
B. 2
C. `1//sqrt(2)`
D. `sqrt(2)`

Answer 1

Correct Answer - D
`A_(1)=A`
`R=sqrt(A_(1)^(2)+A_(2)^(2))`
`=sqrt((A^(2))/(4)+(A^(2))/(4))=sqrt((2A^(2))/(4))=(A)/(sqrt(2))`
`(A_(1))/(R)=(A)/((A)/(sqrt(2)))=(sqrt(2))/(1)`