Simple Harmonic Oscillator

Overview

Engineering reference data for Simple Harmonic Oscillator in miscellaneous.

Key Formulas

Unit Conversion

$y = x \cdot k$

Multiply by conversion factor.

Linear Interpolation

$y = y_1 + \frac{(x - x_1)(y_2 - y_1)}{x_2 - x_1}$

Estimate between two known points.

Percentage

$p = \frac{\text{part}}{\text{whole}} \times 100\%$

Part as fraction of whole.

Variables

Practical Example

To better understand the application of the time period formula, consider this worked example:

Given a mass m = 500 kg attached to a spring with a spring constant k = 16000 N/m, the time period of oscillation can be calculated as follows:

1. Apply the formula: $T = 2\pi \sqrt{\frac{m}{k}}$

2. Substitute the known values: $T = 2\pi \sqrt{\frac{500\ \text{kg}}{16000\ \text{N/m}}}$

3. Simplify the expression inside the square root: $\frac{500}{16000} = 0.03125$ $T = 2\pi \sqrt{0.03125}$

4. Calculate the final value: $\sqrt{0.03125} \approx 0.1768$ $T \approx 2\pi \times 0.1768 \approx 1.11\ \text{s}$

Result: The system completes one full oscillation in approximately 1.1 seconds. This calculation is fundamental in designing systems where predictable oscillatory motion is required, such as in vehicle suspension or vibration isolation systems.

References

• Original Source