Answer the following question What is the inverse of frequency of oscillation of a simple pendulum mounted in a cabin that is freely falling under gravity ?

Answer

To solve the question regarding the inverse of the frequency of oscillation of a simple pendulum mounted in a cabin that is freely falling under gravity, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Scenario**:
- A simple pendulum is attached to the ceiling of a cabin that is in free fall. In free fall, the effective gravitational acceleration acting on the pendulum is zero (g = 0).

2. **Recall the Formula for Time Period**:
- The time period (T) of a simple pendulum is given by the formula:
\[ T = 2\pi \sqrt{\frac{L}{g}} \]
where \( L \) is the length of the pendulum and \( g \) is the acceleration due to gravity.

3. **Substituting g = 0**:
- Since the cabin is in free fall, we substitute \( g = 0 \) into the time period formula:
\[ T = 2\pi \sqrt{\frac{L}{0}} \]
- This expression indicates that we are dividing by zero, which mathematically leads to an undefined result.

4. **Interpret the Result**:
- As \( g \) approaches zero, the time period \( T \) approaches infinity:
\[ T \to \infty \]

5. **Relate Time Period to Frequency**:
- The frequency (f) of oscillation is the reciprocal of the time period:
\[ f = \frac{1}{T} \]
- Therefore, if \( T \) approaches infinity, the frequency \( f \) approaches zero:
\[ f \to 0 \]

6. **Finding the Inverse of Frequency**:
- The inverse of frequency is simply the time period \( T \):
\[ \text{Inverse of frequency} = T \]
- Since we established that \( T \to \infty \), we conclude that the inverse of the frequency of oscillation of the pendulum in free fall is:
\[ \text{Inverse of frequency} = \infty \]

### Final Answer:
The inverse of the frequency of oscillation of a simple pendulum mounted in a cabin that is freely falling under gravity is **infinity**.