A runner’s arm swings rhythmically according to the equation

where y denotes the angle between the actual position of the upper arm and the downward vertical position (as shown in the figure) and where t denotes time (in seconds).

(a) Graph y as a function of t.
(b) Calculate the velocity and the acceleration of the arm.
(c) Verify that the angle y and the acceleration d²y/dt² are related by the differential equation

(d) Apply the fact that the force exerted by the muscle as the arm swings is proportional to the acceleration of y, with a positive constant of proportionality, to find the direction of the force (counterclockwise or clockwise) at t = 1 second, t = 4/3 seconds, and t = 5/3 seconds. What is the position of the arm at each of these times?

Transcribed Image Text:

TT y = cos| 37[ f 32 (−)]. t 8 3