Assertion : The gerph between velocity and displacement for a harmonic oscillation is a parabola
Reason : Velocity does not change uniformly with displacement in simple harmonic motion

Options

A. If both assertion and reason are true and the reasopn is correct explanation of the assertion
B. If both assertion and reason are true and but not the correct explanation of assertion
C. If assertion is true but the reason is false
D. If both assertion and reason are false

Answer

C

Explanation

While executing `SHM` from relation
`v = omega sqrt((A^(2) - y^(2))`
`v^(2) = omega (A^(2) - y^(2))`
`v^(2) = omega^(2) A^(2) -omega^(2) y^(2)`
Dividing both side the `omega^(2) A^(2)`
`(v^(2))/(omega^(2)A^(2)) + (y^(2))/(A^(2)) = 1`...(1)
it is understood that Eq `(1)` repressent the equation of an elipe so the graph between `v` (velocity) and `y` (displacement) is not a perabole
Angle from Eq (1) displacement `(y)` increase the velocity decrease becomes zero at maximum displace and again increase with in `SHM` the velocity Thus with displacement in `SHM` the velocity does not change uniformly