A piston (with mass M) in a car engine is in vertical simple harmonic motion with amplitude A. The engine is running at a period T. Suppose a small piece of metal with mass m were to break loose from the surface of the piston when it (the piston) is at the lowest point z and velocity is v. At what position in meters does the piece of metal lose contact with the piston?
Also the maximum velocity and acceleration are given.
The text book gives these equations:
$x(t) = Acos(wt+φ)$
$v(t) = -wAsin(wt+φ)$
$a(t) = -w^2Acos(wt+φ)$
So I propose that the best way to figure this out would be to solve for the time at which acceleration is at its max, then plug that time into $x(t)$. But I must first solve for the phase constant. Is this correct? If so, how do I find the phase constant?