Simple Harmonic Motion
Explore mass-spring oscillations and energy transformations. Adjust mass, spring constant, and damping to observe how frequency, amplitude, and energy interchange between kinetic and potential forms.
WHAT IS SIMPLE HARMONIC MOTION?
Simple Harmonic Motion (SHM) occurs when an object is acted upon by a restoring force that is directly proportional to its displacement from an equilibrium position (). This leads to periodic, sinusoidal oscillation. Common examples in AP Physics 1 include mass-spring systems and simple pendulums.
CORE FORMULAS
Period of a mass-spring system:\nT_s = 2\pi \sqrt{\frac{m}{k}}\n\nPeriod of a simple pendulum:\nT_p = 2\pi \sqrt{\frac{L}{g}}\n\nWhere:\n- is the period (s)\n- is mass, is spring constant\n- is pendulum length, is gravity
HOW TO USE THIS VISUALIZATION
1. **Choose System**: Toggle between the spring and the pendulum.\n2. **Change Parameters**: Adjust mass, length, or spring constant.\n3. **Start Oscillation**: Displace the object and watch the energy exchange between potential and kinetic.\n4. **Analyze Graphs**: View the position-time and energy-time plots.
CORE FORMULAS
AP EXAM CONNECTION
Unit: Unit 7: Oscillations (Topic 7.1)
Learning Objective: 7.1.1
COMMON MISCONCEPTIONS
- Thinking period depends on amplitude for SHM (it doesn\'t for ideal systems).
- Confusing frequency () with period.
- Applying SHM formulas to pendulums at very large angles (only valid for small angles).
KEY TAKEAWAYS
- Restoring force is proportional to displacement.
- Period is independent of amplitude in ideal SHM.
- Energy oscillates between kinetic and potential.
- Velocity is maximum at equilibrium; acceleration is maximum at peaks.
PRACTICE QUESTIONS
Q1 (QUANTITATIVE): If you quadruple the mass on a spring, how does the period change?
Show Answer & Explanation
Answer: It doubles.
Explanation: . , so the period doubles.
Q2 (CONCEPTUAL): Does the period of a simple pendulum depend on the mass of the bob?
Show Answer & Explanation
Answer: No.
Explanation: The pendulum formula only depends on length and gravity, not mass.
