Simple Harmonic Motion Explorer
Animate a spring-mass system in SHM with real-time x(t), v(t), a(t) graphs. Adjust amplitude, mass, and spring constant to see how period, frequency, and energy change.
WHAT IS SIMPLE HARMONIC MOTION?
Simple Harmonic Motion (SHM) is a type of periodic motion where the restoring force is directly proportional to the displacement from equilibrium and acts in the opposite direction. In AP Physics 1, we primarily study the **mass-spring system** and the **simple pendulum**. The motion is sinusoidal, characterized by its amplitude (maximum displacement), period (time for one cycle), and frequency (cycles per second).
HOW TO USE THIS VISUALIZATION
1. **Adjust the Mass and Spring Constant**: Observe how increasing mass increases the period , while increasing the spring constant decreases it. 2. **Change Amplitude**: Notice that for an ideal spring, changing the amplitude does **not** change the period of oscillation. 3. **Switch to Pendulum**: Adjust the length and observe that the mass does not affect the period of a simple pendulum.
CORE FORMULAS
AP EXAM CONNECTION
Unit: Unit 7: Oscillations (Topic 7.1)
Learning Objective: 7.1.1
COMMON MISCONCEPTIONS
- Thinking the period of a pendulum depends on its mass.
- Believing that a larger amplitude increases the period of an ideal spring.
- Confusing frequency and period units (Hz vs. seconds).
KEY TAKEAWAYS
- Simple Harmonic Motion (SHM) is periodic and sinusoidal.
- The period of a mass-spring system depends on mass and the spring constant.
- The period of a simple pendulum depends only on its length and local gravity ().
- For ideal oscillators, the period is independent of the amplitude.
PRACTICE QUESTIONS
Q1 (QUANTITATIVE): A mass-spring system oscillates with a period . If the mass is quadrupled, what happens to the period?
Show Answer & Explanation
Answer: The period doubles.
Explanation: Since , quadrupling the mass () results in times the original period.
