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The motion of a particle is represented ...

The motion of a particle is represented by the function "A`sin^(2)omegat + Bcos^(2)omegat + Csinomegatcosomega`t".
Where `x,omega` amd t present displacement, angular frequency and time respectively. The constants `A, B` and C are related to the amplitude pf displacement. Select CORRECT alternative(s).

A

for any value of A, B and C (except `C = 0`)

B

If `A = -B, C = 2B`, amplitude `= |Bsqrt(2)|`

C

If `A = B, C = 0`

D

If `A = B, C = 2B`, amplitude `= |B|`

Text Solution

Verified by Experts

The correct Answer is:
A, B, D
For `A = -B` and `C = 2B`
`X = B cos 2omegat + B sin 2omegat = sqrt(2)B sin(2omegat+(pi)/(4))`
This is equation of SHM of amplitude `sqrt(2)B`
If `A = B` and `C = 2B`, then `X = B + B sin 2omegat`
This is also equation of SHM about the point `X = B` function oscillates between `X = 0` and `X = 2B` with amplitude `B`.
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