Is it possible for a body executing linear SHM to have a velocity of 0.03 `ms^(-1)` when its displacement is 0.04 m and a velocity of `0.04 ms^(-1)` , when its displacement is`0.03 m` ? Given amplitude and period of the oscillation are 0.05 m and 6.284 s.
Hint `: v omega sqrt(A^(2)-x^(2))`
or `v^(2) = omega^(2) ( A^(2) - x^(2))`
`0.03^(2) = omega^(2) ( A^(2) - 0.04 ^(2))` ....(1)
`0.04 ^(2) = omega^(2) ( A^(2) - 0.03^(2))` ......(2)
Solve equation (1) and(2) to find a and `omega . T = ( 2pi)/( omega)` . The values of A and T should be same as given values.

Explanation

`v omega sqrt(A^(2)-x^(2))`
or `v^(2) = omega^(2) ( A^(2) - x^(2))`
`0.03^(2) = omega^(2) ( A^(2) - 0.04 ^(2))` ....(1)
`0.04 ^(2) = omega^(2) ( A^(2) - 0.03^(2))` ......(2)
Solve equation (1) and(2) to find a and `omega . T = ( 2pi)/( omega)` . The values of A and T should be same as given values.