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Overview
Grade 11 Functions, University Preparation (MCR3U)
D. Trigonometric Functions
40. 11F.D3.2
40.3 Spring (simple harmonic motion) trig problems
Spring Simple Harmonic Motion Trig Problems
Turn a bouncing spring into a sine or cosine equation. Learn the simple harmonic motion formula and solve real spring problems step by step.
What You'll Learn
A spring bouncing up and down is a classic real-world example of simple harmonic motion that trig functions can model exactly
The position of the mass at time t is given by y equals A cosine of bt or y equals A sine of bt, where A is the amplitude
The period tells you how long one full bounce cycle takes, and it connects to b through the formula b equals 2 pi divided by the period
Choosing sine versus cosine depends only on where the spring starts: at maximum stretch use cosine, at the equilibrium position use sine
The same modeling approach used for a spring also describes Ferris wheels and tide heights, just with different starting conditions
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
Learning resources
Skills
Simple Harmonic Motion
Trigonometric Functions
Negative Cosine
Amplitude
Period
Sinusoidal Modeling
Graphing Technology
ON Curriculum Aligned