Displacement Velocity and Acceleration in Simple Harmonic Motion

Simple Harmonic Motion Simulator - The Science Cube

Simple Harmonic Motion

Ideally Undamped System Visualization

The Science Cube
System View
t = 0.00s
Kinematics Data Plot

Real-Time Telemetry

Physics Insights

Restoring Force: In this ideal system, the mass is subject to a restoring force F = -kx. This linear relationship ensures the acceleration is always directed towards the equilibrium (x = 0).

Phase Relationship: Observe the graph peaks. Velocity (v) leads displacement (x) by 90° (π/2 rad). Acceleration (a) is 180° out of phase with displacement, reaching its maximum positive value when the mass is at its maximum negative displacement.

Conservation of Energy: Notice how velocity is zero at the extremes (±A) where potential energy is maximum, and velocity is at its peak (vₘₐₓ = Aω) at the center (x = 0) where kinetic energy is maximum.

Calculation: ω = 2π/T | Engine: 60Hz Fixed Step

© The Science Cube

Interactive Simple Harmonic Motion (SHM) Simulator

Explore the fundamentals of Simple Harmonic Motion (SHM) with this interactive tool! This simulation visualizes a mass oscillating on a horizontal spring and simultaneously plots its key physical properties in real-time.

How to Use the Simulation:

  • Run & Pause: Use the Start/Stop button to run or pause the animation.
  • Analyze: The Step → button advances the simulation by a small time (0.1s) for careful analysis of the vectors and graph positions.
  • Experiment: Before starting, adjust the parameters in the "Controls" section:
    • Amplitude (A): Sets the maximum displacement from the center (equilibrium) position.
    • Start Pos (x₀): Sets the initial position of the mass at time t = 0. This value must be between -A and +A.
    • Period (T): Sets the total time (in seconds) it takes for one complete oscillation.
    • Graph Duration: Sets the total time (in seconds) shown on the x-axis of the graph below.
  • Restart: Press Reset Simulation to apply your new parameters and return the time to zero.

What Students Can Understand:

This simulation is designed to build an intuitive understanding of the core concepts of SHM by connecting the physical motion of the block to its abstract graphs:

  1. Phase Relationships: Observe the graphs for Displacement (Cyan), Velocity (Red), and Acceleration (Green) all at once. Notice that:
    • When displacement is maximum (at +A or -A), velocity is zero, and acceleration is maximum but in the opposite direction.
    • When displacement is zero (at the center), velocity is at its maximum, and acceleration is zero.
  1. Vector Visualization: The arrows above the block show the instantaneous velocity and acceleration.
    • The red (velocity) vector shrinks as the block approaches an end and grows as it moves toward the center.
    • The green (acceleration) vector always points towards the center equilibrium position and is longest when the block is farthest away (at +A or -A).

Play Around and Discover:

  • What happens to the maximum velocity (the peak of the red graph) if you keep the amplitude the same but decrease the period?
  • Set the Start Pos (x₀) to 0. How do the graphs change compared to starting at x₀ = A? This demonstrates a 90-degree phase shift.
  • Pause the simulation exactly where the green acceleration graph crosses the zero line. Where is the block, and what is its velocity vector doing?

Complete and Continue