Function `x=Asin^(2)omegat+Bcos^(2)omegat+Csinomegat cos omegat` represents simple harmonic motion,

Options

A. Any value of `A,B` and `C` (except `C = 0)`
B. `A =- B, C = 2B`, amplitude `=|Bsqrt(2)|`
C. `A =B, C = 0`
D. `A =B,C = 2B`, amplitude `=|B|`

Answer

A, B, D

Explanation

Using `sin 2 omega =2 sin omegat cos omegat` and
`cos 2omegat =1 -2 sin^(2) omegat =2 cos^(2)omegat -1`.
We get, `x =(A)/(2) (1-cos 2omegat) +(B)/(2) (1_cos 2omegat) +(C )/(2)sin 2 omegat`
For `A =0, B =0, x =(C )/(2)sin 2 omegat`, so choice (a) is correct for `A =-B` and `C=2B, x =B cos 2 omegat +B sin 2 omegat`
Amplitude `=|Bsqrt(2)|` So choice (b) is correct For `A =B,C =0, X =A` Hence ,(c) is not correct option. For `A =B, C = 2B, X = B+B sin omegat` It also represents `SHM` will amplitude `B`. So choice (d) is correct.