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Spring (simple harmonic motion) trig problems
- Lesson: 121:36
Spring (simple harmonic motion) trig problems
Basic Concepts: Sine graph: y = sin x, Cosine graph: y = cos x, Graphing transformations of trigonometric functions
Related Concepts: Reference angle, Find the exact value of trigonometric ratios, ASTC rule in trigonometry (All Students Take Calculus), Converting between degrees and radians
Lessons
- 1.A mass is supported by a spring so that it rests 50 cm above a table top, as shown in the diagram below. The mass is pulled down to a height of 20 cm above the table top and released at time t = 0. It takes 0.8 seconds for the mass to reach a maximum height of 80 cm above the table top. As the mass moves up and down, its height h, in cm, above the table top, is approximated by a sinusoidal function of the elapsed time t, in seconds, for a short period of time.
a)Graph how the height h of the mass varies with respect to the elapsed time t.b)Determine a sinusoidal function that gives the mass's height h above the table top as a function of time t secondsc)What is the height of the mass 1.4 seconds after being released?d)Find the time t when the mass is 70cm above the table top for the third time?
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15.
Applications of Trigonometric Functions
15.1
Ferris wheel trig problems
15.2
Tides and water depth trig problems
15.3
Spring (simple harmonic motion) trig problems