A simple pendulum moves from one end to the other in `1//4` second. What is its frequency?

Answer

To find the frequency of a simple pendulum that moves from one end to the other in \( \frac{1}{4} \) seconds, we can follow these steps:

### Step 1: Understand the Motion of the Pendulum
The pendulum takes \( \frac{1}{4} \) seconds to move from one end to the other. This is half of a complete oscillation (from one extreme to the other).

### Step 2: Calculate the Time Period
The time period \( T \) of the pendulum is the time taken for a complete oscillation (from one end to the other and back). Since it takes \( \frac{1}{4} \) seconds to go from one end to the other, it will take the same amount of time to return. Therefore, the total time period is:
\[ T = \frac{1}{4} \text{ seconds} + \frac{1}{4} \text{ seconds} = \frac{1}{2} \text{ seconds} \]

### Step 3: Calculate the Frequency
The frequency \( f \) is defined as the number of oscillations per second and is given by the formula:
\[ f = \frac{1}{T} \]
Substituting the value of the time period \( T \):
\[ f = \frac{1}{\frac{1}{2}} = 2 \text{ Hz} \]

### Final Answer
The frequency of the pendulum is \( 2 \text{ Hz} \).

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