The velocities of a body executing `SHM` at displacement 'a' and 'b' are 'b' and 'a' respectively. The amplitude of `SHM` is

Options

A. a + b
B. a - b
C. `sqrt(a^(2)+b^(2))`
D. `sqrt(a^(2)-b^(2))`

Answer

C

Explanation

`b = omega sqrt(A^(2) - a^(2))`
`a = omega sqrt(A^(2) - b^(2))`
`(b)/(a) = sqrt((A^(2) - a^(2))/(A^(2) - b^(2))) rArr A = sqrt(a^(2) + b^(2))`