Simple harmonic motion is the projection of uniform circular motion on

Options

A. x-axis
B. y-axis
C. reference circle
D. any diameter of reference circle

Explanation

To solve the question, we need to understand the relationship between simple harmonic motion (SHM) and uniform circular motion (UCM). Here's a step-by-step breakdown of the solution:

### Step 1: Understand Uniform Circular Motion
Uniform circular motion refers to the motion of an object moving in a circle at a constant speed. The object moves around the circumference of the circle, and its position can be described using angles.

**Hint:** Visualize a circle and consider a point moving around it at a constant speed.

### Step 2: Define the Projection
When we talk about the projection of this circular motion, we mean looking at the motion of the object from a specific viewpoint, typically along a straight line (like the x-axis or y-axis).

**Hint:** Think of how a shadow is cast on a wall when a light shines on an object.

### Step 3: Analyze the Projections
As the particle moves around the circle, its position can be projected onto the x-axis and y-axis. The x-axis projection corresponds to the horizontal position of the particle, while the y-axis projection corresponds to the vertical position.

**Hint:** Draw a circle and mark the x and y coordinates of the particle as it moves.

### Step 4: Relate to Simple Harmonic Motion
The projections of the circular motion onto the x-axis or y-axis will oscillate back and forth, which is characteristic of simple harmonic motion. For example, when the particle is at the maximum height on the circle, the projection on the y-axis is maximum, and the projection on the x-axis is zero.

**Hint:** Consider how the sine and cosine functions describe the position of the particle in SHM.

### Step 5: Conclusion
From the analysis, we conclude that simple harmonic motion is indeed the projection of uniform circular motion onto any diameter of the reference circle, which can be the x-axis, y-axis, or any other diameter.

**Hint:** Remember that the key concept is that SHM can be viewed as the shadow or projection of UCM.

### Final Answer
Simple harmonic motion is the projection of uniform circular motion on any diameter of the reference circle.