🎚️ Spring-Mass System

Experiment Details

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📖 About This Experiment

A spring-mass system exhibits simple harmonic motion (SHM) when displaced from equilibrium. The restoring force is proportional to displacement (Hooke's Law: F = -kx), resulting in oscillatory motion. This simulation demonstrates how mass, spring stiffness, and damping affect the system's behavior.

The energy continuously transforms between potential energy (stored in the spring) and kinetic energy (motion of the mass), while the total energy remains constant in the absence of damping.

📐 Key Formulas

Period:T = 2π√(m/k)

Time for one complete oscillation

Frequency:f = 1/T = (1/2π)√(k/m)

Oscillations per second (Hertz)

Hooke's Law:F = -kx

Restoring force proportional to displacement

Angular Frequency:ω = √(k/m)

Rate of change of the phase of the oscillation

Kinetic Energy:KE = ½mv²

Energy due to motion

Potential Energy:PE = ½kx²

Energy stored in the spring

💡 Key Concepts

  • •
    Simple Harmonic Motion (SHM): Periodic motion where the restoring force is proportional to displacement and acts in the opposite direction.
  • •
    Equilibrium Position: The point where the net force on the mass is zero (spring is neither stretched nor compressed).
  • •
    Amplitude: Maximum displacement from equilibrium. The period is independent of amplitude for small oscillations.
  • •
    Damping: Any resistance that dissipates energy from the system, causing the amplitude to decrease over time.
  • •
    Energy Conservation: In an undamped system, total mechanical energy (KE + PE) remains constant throughout the motion.

🔬 Real-World Applications

  • ▸Automotive Suspension: Car shock absorbers use spring-mass-damper systems to smooth rides.
  • ▸Earthquake Protection: Tuned mass dampers in buildings reduce sway during seismic activity.
  • ▸Timekeeping: Mechanical watches use balance springs and oscillators for precision.
  • ▸Mattress Design: Pocket spring mattresses use individual spring units for comfort.
  • ▸Musical Instruments: Piano and guitar strings vibrate as spring-mass systems to produce sound.

🎮 How to Use This Experiment

  • 1.Adjust the Mass to see how heavier objects oscillate more slowly.
  • 2.Change the Spring Constant to make the spring stiffer or more flexible.
  • 3.Modify Damping to simulate friction and air resistance.
  • 4.Set the Initial Displacement to determine starting position.
  • 5.Use Play/Pause to control the simulation and Reset to restart.
  • 6.Watch the Energy Bar to see KE and PE exchange in real-time.
🚀 Launch Experiment