In physics, it can be shown that a particle forced to oscillate in a resisting medium has amplitude A(r) given by

where r is the ratio of the forcing frequency to the natural frequency of oscillation and k is a positive constant that measures the damping effect of the resisting medium. Show that A(r) has exactly one positive critical number. Does it correspond to a relative maximum or a relative minimum? Can anything be said about the absolute extrema of A(r)?

Transcribed Image Text:

A(r) = 1 (1 - r²)² + kr²