Displacement Velocity and Acceleration in Simple Harmonic Motion

Simple Harmonic Motion – The Science Cube
t = 0.00 s
Kinematics Plot
Real-Time Telemetry
Physics Insights

System Dynamics: The oscillation period is dictated by T = 2π√(m/k). Notice how increasing the mass (m) increases inertia, lengthening the period, whereas a stiffer spring (higher k) speeds up the oscillation.

Restoring Force & Vectors: The acceleration vector (navy) strictly obeys a ∝ -x, always pointing toward equilibrium. The velocity vector (orange) leads displacement by 90°.

Energy Bar Chart: Mechanical energy is conserved: E = ½kx² + ½mv². Watch the live energy bars on the canvas to see potential (PE) and kinetic (KE) energies exchange perfectly while total energy (TE) remains constant.

ω = √(k/m)  |  T = 2π√(m/k)  |  Engine: 60 Hz fixed step

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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