Sol:- Time taken for 5 oscillations= 10 sec. Time taken for 1 oscillation= 10 sec÷5 = 2 secondTime period of this pendulum is 2 seconds.

Time Period of a Pendulum

To find the time period of a pendulum, we need to understand a few key concepts and formulas. Let's break it down step by step.

1. Time Period:
The time period of a pendulum is the time taken for one complete oscillation or swing. It is denoted by the symbol T.

2. Given Information:
In this case, we are given that a simple pendulum takes 10 seconds to complete 5 oscillations. This means that in 10 seconds, the pendulum swings back and forth five times.

3. Calculation of Time Period:
To find the time period, we divide the total time taken by the number of oscillations. In this case, the total time taken is 10 seconds, and the number of oscillations is 5.

Time Period (T) = Total Time (t) / Number of Oscillations (n)

Substituting the given values:
T = 10 seconds / 5 oscillations
T = 2 seconds

Hence, the time period of this simple pendulum is 2 seconds.

Explanation:
A pendulum consists of a mass attached to a fixed point with a string or rod. When the mass is displaced from its equilibrium position and released, it swings back and forth, undergoing periodic motion.

The time period of a pendulum depends on two factors: the length of the string or rod (l) and the acceleration due to gravity (g).

Mathematical Formula:
The time period of a simple pendulum can be calculated using the following formula:

T = 2π √(l/g)

Where:
T = Time period of the pendulum
π = Pi (approximately 3.14159)
l = Length of the pendulum
g = Acceleration due to gravity (approximately 9.8 m/s²)

In this case, we are not given the length of the pendulum or any other information to directly calculate the time period using the formula. Instead, we are given the time taken for a specific number of oscillations. Therefore, we use the simplified formula mentioned earlier:

T = Total Time (t) / Number of Oscillations (n)

Summary:
In summary, the time period of a simple pendulum can be calculated by dividing the total time taken by the number of oscillations. In this case, the given pendulum takes 10 seconds to complete 5 oscillations, resulting in a time period of 2 seconds.