Which of the following motions is not simple harmonic?

Options

A. Vertical oscillations of a spring
B. Motion of a simple pendulum
C. Motion of planet around the sun
D. Oscillation of liquid in a U-tube

Explanation

To determine which of the following motions is not simple harmonic motion (SHM), we need to analyze each option based on the definition of SHM. Simple harmonic motion is characterized by a restoring force that is directly proportional to the displacement from the mean position.

### Step-by-Step Solution:

1. **Understanding Simple Harmonic Motion (SHM)**:
- SHM occurs when the restoring force acting on an object is directly proportional to its displacement from the equilibrium position and acts in the opposite direction.

2. **Analyzing Option 1: Vertical Oscillation of a Spring**:
- When a mass is attached to a spring and displaced from its equilibrium position, the restoring force (F) is given by Hooke's Law: \( F = -kx \), where \( k \) is the spring constant and \( x \) is the displacement.
- Since the restoring force is directly proportional to the displacement, this motion is SHM.

3. **Analyzing Option 2: Motion of a Simple Pendulum**:
- For a simple pendulum, when displaced by a small angle \( \theta \), the restoring torque is proportional to \( \theta \) (i.e., \( \tau = -mgL\theta \)).
- This also results in SHM for small angles, as the restoring force is proportional to the displacement from the mean position.

4. **Analyzing Option 3: Motion of a Planet Around the Sun**:
- The motion of a planet around the Sun is not oscillatory in nature. Instead, it follows an elliptical orbit due to gravitational attraction and does not oscillate about a mean position.
- Thus, this motion does not satisfy the criteria for SHM.

5. **Analyzing Option 4: Oscillation of a Liquid in a U-tube**:
- When a liquid is displaced in a U-tube, the restoring force due to gravity acts to bring the liquid back to its equilibrium position.
- The restoring force is proportional to the displacement, indicating that this motion is also SHM.

### Conclusion:
Based on the analysis, the motion that is **not** simple harmonic is:
- **Option 3: Motion of a planet around the Sun.**