1. What is Simple Harmonic Velocity?

The velocity in simple harmonic motion describes how fast the oscillating object is moving and in what direction at any given time. It varies sinusoidally with time and reaches maximum magnitude when the displacement is zero.

2. How Does the Calculator Work?

The calculator uses the simple harmonic velocity equation:

Where:

• \( v \) — Velocity (m/s)
• \( A \) — Amplitude (m)
• \( \omega \) — Angular frequency (rad/s)
• \( t \) — Time (s)
• \( \phi \) — Phase angle (rad)

Explanation: The negative sign indicates that the velocity is in the opposite direction to the displacement when the object is moving back toward the equilibrium position.

3. Importance of Velocity Calculation

Details: Calculating velocity in simple harmonic motion is essential for understanding energy transformations (between kinetic and potential energy), determining maximum speed, and analyzing phase relationships between displacement, velocity, and acceleration.

4. Using the Calculator

Tips: Enter all values in SI units. Amplitude and angular frequency must be positive. Phase angle can be positive or negative. Time must be ≥0.

5. Frequently Asked Questions (FAQ)

Q1: What's the relationship between velocity and displacement in SHM?
A: Velocity is 90° out of phase with displacement. When displacement is maximum, velocity is zero, and vice versa.

Q2: What is the maximum velocity in SHM?
A: The maximum velocity is \( v_{max} = A\omega \), occurring when the object passes through the equilibrium position.

Q3: How does angular frequency relate to frequency?
A: Angular frequency \( \omega = 2\pi f \), where \( f \) is the frequency in Hz.

Q4: What does negative velocity mean?
A: Negative velocity indicates motion in the opposite direction of the positive displacement direction defined by the coordinate system.

Q5: Can this equation be used for any oscillating system?
A: This applies to ideal simple harmonic oscillators where the restoring force is proportional to displacement (Hooke's Law).