Question

When are the velocity and acceleration in the same direction in shm

Answer 1

x = A sin w t          an equation for SHM

v = w A cos w t

a = - w^2 A sin wt

a / v = -w tan w t

So when tan (w t ) is negative both a and v will have the same sign.

This occurs in the 2d and 4d quadrants.

For instance, in the second quadrant when the object is returning towards

the origin, v will be in the negative direction and the acceleration is decreasing from its maximum negative value.