1. What is Simple Harmonic Motion?

Simple Harmonic Motion (SHM) is a type of periodic motion where the restoring force is directly proportional to the displacement. It's commonly observed in spring-mass systems and pendulums (for small angles).

2. How Does the Calculator Work?

The calculator uses the SHM frequency equation:

Where:

• \( \omega \) — Angular frequency (rad/s)
• \( k \) — Spring constant (N/m)
• \( m \) — Mass (kg)

Explanation: The angular frequency determines how fast the system oscillates. Higher spring constants or smaller masses result in higher frequencies.

3. Importance of Angular Frequency

Details: Angular frequency is crucial for understanding the dynamics of oscillating systems, calculating periods of oscillation, and designing mechanical systems with specific vibration characteristics.

4. Using the Calculator

Tips: Enter spring constant in N/m and mass in kg. Both values must be positive numbers. The calculator will compute the angular frequency in radians per second.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between angular frequency and regular frequency?
A: Angular frequency (ω) is measured in rad/s, while regular frequency (f) is in Hz. They're related by ω = 2πf.

Q2: Does this equation work for all spring-mass systems?
A: It works for ideal springs obeying Hooke's law with negligible damping and massless springs.

Q3: How does gravity affect this calculation?
A: Gravity doesn't affect the angular frequency in a horizontal spring-mass system. For vertical systems, it only changes the equilibrium position.

Q4: What if my spring doesn't obey Hooke's law perfectly?
A: This calculation becomes less accurate for non-linear springs or large displacements.

Q5: Can I calculate the period from this result?
A: Yes, the period T = 2π/ω.