Question

The position of a car piston within the cylinder is described by the equation:
y = S sin(360

r t - 90
Where S is the stroke length of the cylinder, r is the rpm of the crank shaft, and t is
the time in minutes. If the stroke length is 2 inches and the crank shaft is running at
1300 rpm, find the position of the piston at t = 53 seconds. (remember that rpm
means revolutions per minute)

Answer 1

what's the problem?

y(t) = S sin(360rt-90)
S = 2
r = 1300
t = 53/60

y(53/60) = 2sin(360*1300*53/60-90)
= 2sin(1148.3333*360 - 90)
now, we can toss out all multiples of 360, so we are left with
y = 2sin(240-90) = 2sin(150) = 2(.5) = 1.0

Answer 2

oops.

y = 2sin(120-90) = 2sin(30) = 2(.5) = 1.0