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### Question 8:
(a) **(i)** *State the reason why simple harmonic motion is periodic.*
- **Answer**: Simple harmonic motion (SHM) is periodic because the restoring force is proportional to the displacement and acts in the opposite direction. This leads to oscillations that repeat at regular time intervals, meaning the motion follows a consistent pattern or cycle.

**(ii)** *State two factors that affect the period of oscillation of a simple pendulum.*
- **Answer**: 
   1. The **length of the pendulum**: The period increases as the length increases.
   2. The **acceleration due to gravity (g)**: The period decreases if the gravitational force is stronger (for example, on a planet with stronger gravity).

(b) **(iii)** *Sketch a graph of the total mechanical energy, E, against displacement, y, for the motion of a simple pendulum from one extreme position to the other.*
- **Explanation**: The total mechanical energy of a simple pendulum is the sum of its potential and kinetic energies. It remains constant throughout the motion. At maximum displacement (the extreme positions), the energy is entirely potential. At the center, the energy is entirely kinetic. 
  - A suitable graph would show a constant horizontal line since the total mechanical energy doesn't vary with displacement, assuming no energy losses like friction.

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### Related Questions:
1. What is the relationship between the amplitude of oscillation and the period of a simple harmonic oscillator?
2. How does damping affect the periodic motion of a pendulum?
3. What are the conditions required for an oscillatory motion to be classified as simple harmonic motion?
4. Can the simple harmonic motion equation be applied to a mass-spring system? If so, how?
5. How does the total mechanical energy of a simple pendulum change when energy losses like air resistance are considered?

### Tip:
The period of a simple pendulum is independent of its mass, and depends only on the length and local gravitational acceleration.

State the reason why simple harmonic motion is periodic. State two factors that affect the period of oscillation of a simple pendulum. Sketch a graph of the total mechanical energy, E, against displacement, y, for the motion of a simple pendulum from one extreme position to the other.

Learn why simple harmonic motion is periodic, explore factors that affect the oscillation period of a simple pendulum, and sketch a graph of mechanical energy against displacement. Suitable for high school physics students.

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