1. What is the Amplitude Velocity Formula?

The amplitude velocity formula calculates the velocity of an object in simple harmonic motion at a specific displacement from the equilibrium position. It's derived from the conservation of energy principle in oscillatory systems.

2. How Does the Calculator Work?

The calculator uses the amplitude velocity formula:

Where:

• \( v \) — Velocity (m/s)
• \( \omega \) — Angular frequency (rad/s)
• \( A \) — Amplitude (m)
• \( x \) — Displacement from equilibrium (m)

Explanation: The formula shows that velocity is maximum at equilibrium (x=0) and zero at maximum displacement (x=A).

3. Importance of Velocity Calculation

Details: Calculating velocity in harmonic motion is essential for understanding energy distribution, predicting motion patterns, and designing oscillatory systems like springs and pendulums.

4. Using the Calculator

Tips: Enter angular frequency in rad/s, amplitude in meters, and displacement in meters. All values must be valid (ω > 0, A > 0, 0 ≤ x ≤ A).

5. Frequently Asked Questions (FAQ)

Q1: What is simple harmonic motion?
A: Simple harmonic motion 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.

Q2: When is velocity maximum in harmonic motion?
A: Velocity is maximum when the object passes through the equilibrium position (x=0), where all energy is kinetic.

Q3: What happens when x = A?
A: When displacement equals amplitude (x=A), velocity becomes zero as the object momentarily stops before reversing direction.

Q4: Can displacement be greater than amplitude?
A: In ideal simple harmonic motion, displacement cannot exceed amplitude as it represents the maximum displacement from equilibrium.

Q5: How is angular frequency related to period?
A: Angular frequency (ω) is related to period (T) by the formula ω = 2π/T, where T is the time for one complete oscillation.