Three simle harmionic motions in the same direction having the same amplitude (a) and same period are superposed. If each differs in phase from the next by `45^@`, then.

Options

A. (i), (ii)
B. (ii), (iii)
C. (i), (iii)
D. (i), (iv)

Answer

C

Explanation

`x_1=asinomegat`,
`x_2=asin(omegatt+pi/4)`, `x_3=asin(omegat+pi/2)`
`x=x_1+x_2+x_3=Asin(omegat+theta)`

Resultant amplitude `=sqrt2a+a=(sqrt2+1)a=A`
`theta=pi/4`
`x=(sqrt2+1)asin(omegat+pi/4)`
`E^'/E=A^2/a^2=(sqrt2+1)^2=2+1+2sqrt2=3+2sqrt2`