1. What is Phase Constant in SHM?

The phase constant (φ) in simple harmonic motion determines the initial position of the oscillating object at time t=0. It represents the phase angle that specifies where in its cycle the oscillation begins.

2. How Does the Calculator Work?

The calculator uses the phase constant formula:

Where:

• \( \varphi \) — Phase constant (radians)
• \( v_0 \) — Initial velocity (m/s)
• \( \omega \) — Angular frequency (rad/s)
• \( A \) — Amplitude (m)

Explanation: The formula calculates the initial phase angle based on the ratio of initial velocity to the product of angular frequency and amplitude.

3. Importance of Phase Constant

Details: The phase constant is crucial for determining the complete solution of simple harmonic motion equations. It affects the initial conditions and helps predict the exact position and velocity of the oscillating system at any given time.

4. Using the Calculator

Tips: Enter initial velocity in m/s, angular frequency in rad/s, and amplitude in meters. All values must be positive, with angular frequency and amplitude greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the range of phase constant values?
A: Phase constant typically ranges from -π to π radians (-180° to 180°), representing the complete cycle of oscillation.

Q2: How does phase constant affect the motion?
A: It determines the starting point of the oscillation in its cycle, affecting both position and velocity at time zero.

Q3: Can phase constant be zero?
A: Yes, when initial velocity is zero, the phase constant is typically zero, meaning the oscillation starts at maximum displacement.

Q4: What units should I use for inputs?
A: Use consistent SI units: meters for amplitude, meters/second for velocity, and radians/second for angular frequency.

Q5: How is this different from phase angle?
A: Phase constant is the initial phase angle at t=0, while phase angle varies with time as ωt + φ during oscillation.