Explain periodic motion and oscillatory motion with illustrations.

Answer

### Step-by-Step Text Solution

**Step 1: Define Periodic Motion**
Periodic motion is defined as motion that repeats itself after a fixed interval of time. This means that the motion occurs in a regular cycle, and the time taken to complete one full cycle is known as the time period (T).

**Illustration for Periodic Motion:**
Consider a person commuting from home to office. If a person leaves home at 8 AM, reaches the office by 9 AM, and then leaves the office at 5 PM to return home by 6 PM, this routine repeats every day. The journey from home to office and back is an example of periodic motion because it occurs at regular intervals.

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**Step 2: Define Oscillatory Motion**
Oscillatory motion is a specific type of motion where an object moves back and forth around a fixed point, known as the mean position. The motion is characterized by the object moving to one side of the mean position and then returning to the other side.

**Illustration for Oscillatory Motion:**
Imagine a ball placed in a frictionless bowl. If the ball is released from one side of the bowl, it rolls to the bottom and then rises to the same height on the opposite side before rolling back. This to-and-fro movement around the mean position (the lowest point of the bowl) exemplifies oscillatory motion.

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**Step 3: Relationship Between Periodic and Oscillatory Motion**
While all oscillatory motions are periodic, not all periodic motions are oscillatory. For example, the motion of the Earth around the Sun is periodic but not oscillatory. However, simple harmonic motion is a special case that exhibits both periodic and oscillatory characteristics.

**Example of Simple Harmonic Motion:**
A classic example of simple harmonic motion is a pendulum swinging back and forth. The pendulum moves to one side, returns to the center (mean position), and then moves to the opposite side, repeating this cycle in a regular time interval.

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