The time period of oscillation of a simple pendulum is the time taken for the pendulum to complete one full cycle or oscillation. It is influenced by various factors such as the length of the pendulum, gravitational acceleration, and the angle of displacement. In this scenario, the car is accelerating horizontally, which can affect the time period of the pendulum.

1. Time period of a simple pendulum:
The time period of a simple pendulum can be calculated using the formula:

T = 2π√(L/g)

Where:
T = time period of the pendulum
π = pi (approximately 3.14159)
L = length of the pendulum
g = gravitational acceleration (approximately 9.8 m/s² on Earth)

2. Effect of acceleration on the pendulum:
When the car accelerates in a horizontal direction, it creates an inertial force acting on the pendulum. This inertial force can affect the motion of the pendulum and hence its time period.

3. Equivalence of gravitational acceleration and inertial force:
In this scenario, we can consider the inertial force acting on the pendulum due to the car's acceleration as equivalent to the gravitational force. This is known as the principle of equivalence.

4. Adjusted effective gravitational acceleration:
The effective gravitational acceleration experienced by the pendulum can be calculated by subtracting the inertial force (due to car acceleration) from the actual gravitational acceleration.

g' = g - a

Where:
g' = effective gravitational acceleration
g = actual gravitational acceleration
a = acceleration of the car

5. Adjusted time period of the pendulum:
Using the adjusted effective gravitational acceleration (g'), we can calculate the adjusted time period (T') of the pendulum using the same formula as before:

T' = 2π√(L/g')

6. Conclusion:
In conclusion, when a car accelerates horizontally, it affects the time period of a simple pendulum hung from the ceiling. The inertial force created by the car's acceleration is considered equivalent to the gravitational force, and the effective gravitational acceleration is adjusted accordingly. This adjustment leads to a change in the time period of the pendulum, which can be calculated using the adjusted effective gravitational acceleration.