Question

A fan with a diameter of 10cm is spinning at 25 revolutions per minute clockwise. The fan's reference blade starts pointing directly upwards. Determine an equation for a sinusoidal function that represents the fan's reference blade's vertical distance from the center (a negative value being accepted). State the period, amplitude and vertical shift for this function.

Answer 1

since t=0 when y is a max, we will have

y = a cos(kt)

the radius is 5, so

y = 5cos(kt)

the period is 1/25 min, so k/2pi = 1/25
k = 2pi/25, and thus

y = 5cos(2pi/25 t)