Functions Math Question

Question

In a car’s engine, there are pistons that move up and down due to combustion. The distance that a piston travels from the resting position (middle h = 0) to each end is 10 cm. In 6 seconds, it repeats its movement of top-to-bottom-to-top 2 times. At what time, is the piston at 4cm above the starting position if the piston starts from the middle and starts moving down first,

Answer 1

A = amplitude = 5

B=2pi/period = 2pi/6/2= 2pi/3

C = phase shift =

D = midline = 0

h(t) = AsinB(t-C) + D

= 5sin[(2pi/3)(t)]

h(t) = 5sin[2pi/3)(t)] = 4

sin2tpi/3 = 4/5

2tpi/3 = sin^-1(4/5) = 53.13

t = 53.13(3/2pi) = 25.37 seconds

but as the period = 3 seconds

it's also at 4 cm in ..., 22.37, 19.37, 16.37, 13.37, 10.37, 7.37, 4.37, 1.37 seconds

or t= 1.37 + 3n seconds where n= any integer