Question

An object performs simple harmonic motion between points k an L with a period 40pi if the distance between k and L is 10cm what is the speed of object when it is 8cm away from equilbrium position?

Answer 1

It is impossible for the object to be 8 cm away from its equilibrium position, as I pointed out in a comment some time ago.

Explanation:

In general, the speed of a particle undergoing a SHM of amplitude `A` and angular frequency `omega` is given by

`v = omega sqrt(A^2-x^2)`

where `x` is the distance of the object from the equilibrium point.

Here `omega = (2pi)/T = 1/20`.

The distance between `K` and `L` is equal to `2A` so that `A = 5\ "cm"`. It is impossible for `x` to be 8 cm for such a motion , since `|x| <= A`