A simple pendulum is suspended from the ceiling a car accelerating uniformly on a horizontal road. If the acceleration is `a_0` and the length of the pendulum is l, find the time period of small oscillations about the mean position.

Explanation

To find the time period of small oscillations of a simple pendulum suspended from the ceiling of a car that is accelerating uniformly, we can follow these steps:

### Step 1: Understand the Effective Gravity
When the car accelerates with an acceleration \( a_0 \), the pendulum experiences a pseudo force acting in the opposite direction of the acceleration. This alters the effective gravitational field acting on the pendulum.

### Step 2: Determine the Effective Acceleration
The effective acceleration \( g_{\text{effective}} \) can be calculated using the Pythagorean theorem because the gravitational force and the pseudo force act perpendicular to each other. Thus, we have:
\[
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