Section 6.8: Applications of SHM
Simple Harmonic Motion (SHM) is not just a mathematical model — it has many real-world applications in science, engineering, and technology. Systems that approximate SHM are useful because their motion is predictable and well understood.
Common Applications:
- Pendulums: Used in clocks for timekeeping.
- Mass-spring systems: Basis for vibration absorbers and vehicle suspensions.
- Electromagnetic oscillations: LC circuits in radios and electronics.
- Seismology: Earthquake waves modeled as oscillatory motion.
- Medical applications: Imaging and resonant scanning devices.
Example 1
A grandfather clock uses a pendulum of length \( L = 0.994 \,\text{m} \). Show that its period is close to 2.00 s, making it suitable for timekeeping.
Period of a simple pendulum:
\[ T = 2\pi \sqrt{\frac{L}{g}} \]Substitute values:
\[ T = 2\pi \sqrt{\frac{0.994}{9.8}} \approx 2.00 \,\text{s} \]This matches the required timekeeping interval.
Practice Problems
- Explain how car suspension systems rely on SHM principles.
- A child’s swing of length 2.5 m is displaced slightly and released. Find its approximate period.
- Why are LC circuits considered oscillatory systems similar to SHM?
- Describe one way SHM applies in medical imaging technology.
- Discuss why an understanding of SHM is important in designing earthquake-resistant buildings.