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Trigonometry
5. Applications of Trigonometric Functions
5.3 Spring (simple harmonic motion) trig problems
Spring (simple harmonic motion) trig problems
What You'll Learn
Model simple harmonic motion of a spring using negative cosine functions
Determine amplitude, period, and midline from physical spring motion data
Calculate height at any given time using sinusoidal equations
Identify parameters a, b, c, and d in the equation y = -a cos(bx - c) + d
Use graphing technology to find intersection points and solve for specific times
What You'll Practice
1
Writing sinusoidal equations from spring motion scenarios
2
Finding height values at specific times using the model
3
Determining when the mass reaches a given height for the nth time
4
Calculating period from maximum and minimum points
Why This Matters
Understanding spring motion through trigonometry connects math to physics and engineering. These skills are essential for modeling periodic phenomena in mechanical systems, sound waves, and oscillations you'll encounter in advanced STEM courses and real-world applications.
Before You Start — Make Sure You Can:
This Unit Includes
1 Video lesson
Skills
Simple Harmonic Motion
Trigonometric Functions
Negative Cosine
Amplitude
Period
Sinusoidal Modeling
Graphing Technology
