Hi all, I was wondering is you could help me with this springs question. We've only done springs hanging from a fixed support above being stretched, but now I've got a question where the spirng is being compressed. 1. The problem statement, all variables and given/known data So, here's some basic info about the question Obviously, acceleration due to gravity is 9.8 m/s^2 The downward direction is considered the positive direction A spring is placed on a fixed support standing vertically The natural length of the spring is 5 metres An iron ball weighing 5kg is attached to the top of it This mass compresses the spring by 0.392m The ball is pulled to a distance of 0.4m above its equalibirum position then released Damping force is proportional to the instantaneous velocity of the ball y(t)=The displacement of the ball below the equalibrium position at t seconds after the release 2. Relevant equations So, the first question is to proove that the equation of motion for the ball is... [itex]0=y''(t)+(b/5)y'(t)+25y(t)[/itex], where b kg/s is the damping constant 3. The attempt at a solution Here is a rough diagram of what I believe to be happening from the description of the problem: So, with Hooke's law [itex]T=mg[/itex] [itex]ks=mg[/itex] (equation 1) [itex]k=mg/s[/itex] [itex]k=(5*9.8)/(-0.392)[/itex] [itex]k=-125[/itex] With Newton's law of motion (F=ma): [itex]m*y''(t)=mg-T-R[/itex] [itex]m*y''(t)=mg-k(s+y(t))-by'(t)[/itex] [itex]m*y''(t)=mg-ks-ky(t)-by'(t)[/itex], from equation 1: ks-mg=0 so [itex]m*y''(t)+ky(t)+by'(t)=0[/itex], So subbing in k=-125, m=5 [itex]5*y''(t)-125y(t)+by'(t)=0[/itex] [itex]y''(t)+b/5y'(t)-25y(t)=0[/itex] This is almost what I need, but for some reason I have -25y(t) instead of +25y(t). Can anyone see where I've gone wrong? The only thing I can think of is that k (and thus s) should be positive, but I am unsure why as it is in compression. We have been taught that stretching (extension) of the spring make "s" a postive number, so one would think that compression of the spring would make give "s" a negative value. Is k always > 0 by definition?