1. The problem statement, all variables and given/known data I'm trying to come up with a problem and solve it. As of right now, I have a vertical spring with an equilibrium length of .38 m hanging. A .61 kg mass is attached to the bottom, and the new equilibrium length is 1.05 m. If the spring is compressed .1 m upwards then pushed down with a velocity of 4.06 m/s, how would you write position as a function of time, as well as velocity and acceleration? 2. Relevant equations Force constant: k = F/x = (mg)/x = (.61 kg * 9.81 m/s^1)/(1.05 m - .38 m) = 8.931 N/M Period: T = 2pi(m/k)^(1/2) T = tpi(0.61kg/8.931 N/M)^(1/2) = 1.642 s^-1 w = 2pif f = 1/T x(t) = Acos(wt) 3. The attempt at a solution I solved for x(t) without any initial velocity. I came up with w = 3.826 s^-1, and an equation of x(t) = -.1cos(3.826t) This may be a dumb question, but would adding the initial velocity just be x(t) = Acos(wt) + vt, where v = 4.06 m/s? What about units? Would it contribute towards angular velocity? Is the -.1 the correct sign for being pushed upwards? I feel confident taking derivatives, so velocity and acceleration I have no problem with getting. It's just the position function I'd like to clarify first.