A simple pendulum is suspended from the roof of a school bus which moves in a horizontal direction with an acceleration a, then the time period is

The time period of a simple pendulum is given by the formula T = 2π√(l/g), where l is the length of the pendulum and g is the acceleration due to gravity.

However, when the bus is accelerating horizontally, this creates a pseudo force in the opposite direction of the acceleration of the bus. This pseudo force changes the effective gravity acting on the pendulum.

The effective gravity (geff) is the resultant of the actual gravity (g) and the pseudo force due to the acceleration of the bus (a). Since these two forces are perpendicular, we can use Pythagoras' theorem to find the resultant:

geff = √(g² + a²)

Substituting this into the formula for the time period gives:

T = 2π√(l/geff) = 2π√(l/√(g² + a²))

So, the time period of the pendulum increases when the bus is accelerating. This is because the effective gravity is larger, so the pendulum swings slower.