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 and acts in the direction opposite to that of displacement. It's a fundamental concept in physics that describes many oscillatory systems.

2. How Does the Calculator Work?

The calculator uses the SHM equation:

Where:

• \( x \) — Displacement from equilibrium position (m)
• \( A \) — Amplitude of motion (m)
• \( \omega \) — Angular frequency (rad/s)
• \( t \) — Time (s)
• \( \phi \) — Phase angle (rad)

Explanation: The equation describes how the displacement varies sinusoidally with time for a system in simple harmonic motion.

3. Importance of SHM Calculations

Details: SHM calculations are crucial for understanding oscillatory systems like springs, pendulums, and many wave phenomena in physics and engineering.

4. Using the Calculator

Tips: Enter amplitude in meters, angular frequency in radians per second, time in seconds, and phase angle in radians. All values must be valid numbers.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between angular frequency and frequency?
A: Angular frequency (ω) is measured in radians per second and equals 2π times the frequency (f) which is measured in Hertz (cycles per second).

Q2: How is phase angle determined?
A: Phase angle depends on initial conditions. At t=0, if displacement is maximum, φ=0; if at equilibrium, φ=π/2.

Q3: What are some examples of SHM systems?
A: Mass-spring systems, simple pendulums (for small angles), LC circuits, and many molecular vibrations exhibit SHM.

Q4: What's the relationship between period and angular frequency?
A: Period (T) = 2π/ω. The period is the time for one complete oscillation.

Q5: Can this calculator be used for damped harmonic motion?
A: No, this calculator is for simple (undamped) harmonic motion. Damped systems require additional terms in the equation.