A particle executes simple harmonic motion with a frequency f. The frequency with which its kinetic energy oscillates is

Options

A. `f/2`
B. f
C. 2 f
D. 4 f

Explanation

To solve the problem, we need to determine the frequency with which the kinetic energy of a particle executing simple harmonic motion (SHM) oscillates.

### Step-by-Step Solution:

1. **Understanding Simple Harmonic Motion (SHM)**:
- A particle in SHM oscillates back and forth around an equilibrium position. The motion is periodic and can be described using a sine or cosine function.

2. **Identifying Key Quantities**:
- The frequency of the SHM is given as \( f \). This means that the particle completes \( f \) cycles in one second.

3. **Kinetic Energy in SHM**:
- The kinetic energy (KE) of a particle in SHM is given by the formula:
\[ KE = \frac{1}{2}mv^2 \]
- Here, \( m \) is the mass of the particle and \( v \) is its velocity.

4. **Behavior of Kinetic Energy**:
- As the particle moves, its kinetic energy oscillates. It reaches a maximum value when the particle passes through the equilibrium position and becomes zero at the extreme positions of the motion.

5. **Frequency of Kinetic Energy Oscillation**:
- In one complete cycle of SHM, the kinetic energy reaches its maximum value twice: once when the particle is moving towards the equilibrium position and once when it is moving away from it.
- Therefore, in one full cycle (which corresponds to the frequency \( f \)), the kinetic energy oscillates from maximum to zero and back to maximum, resulting in two peaks of kinetic energy.

6. **Calculating the Frequency of Kinetic Energy**:
- Since the kinetic energy reaches its maximum twice in one complete cycle of the motion, the frequency of the oscillation of the kinetic energy is:
\[ \text{Frequency of KE oscillation} = 2f \]

### Final Answer:
The frequency with which the kinetic energy oscillates is \( 2f \).

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