M.AMM.27
Determine or analyze an appropriate cyclical model for problem situations that can be modeled with trigonometric functions (e.g., predator-prey models, tide heights, diurnal cycle, and/or music).
Example Problems
The displacement in µm of a loudspeaker diaphragm can be modeled by:
At s the diaphragm passes through equilibrium moving outward, and 0.001 s later it reaches its first maximum of 0.008 µm.
Find , where t is in radians.
At s the diaphragm passes through equilibrium moving outward, and 0.001 s later it reaches its first maximum of 0.008 µm.
Find , where t is in radians.
A rotating lighthouse beam shines on a distant sensor. The light intensity in arbitrary units can be modeled by:
At s the intensity is (maximum). Two-and-a-half seconds later it falls to (minimum).
Find , where is in radians.
At s the intensity is (maximum). Two-and-a-half seconds later it falls to (minimum).
Find , where is in radians.
A mass on a spring oscillates horizontally. Its displacement in m from equilibrium can be modeled by:
At s the mass is at maximum extension, 0.15 m. It first passes equilibrium 0.4 s later.
Find , where is in radians.
At s the mass is at maximum extension, 0.15 m. It first passes equilibrium 0.4 s later.
Find , where is in radians.
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