I am running the student version of maple, the one for hundred, and my final question is wondering if we could solve second order de as in a spring mass system.

The problem reads,  a mass weighing 32 lb stretches a spring 2 ft. The mass is initially relesed from a point 1 foot above equilibrium position with an upward velocity of 2 ft/s

I need to find the amplitude and period of motion and also, how many complete cycles the mass have completed at the end of the 4pi seconds.

So, I am going to make the differential equation to satisfy this theory, I am pretty sure this is a simple harmonic motion problem. If that is the case than the de should be y''+k/m (x) = 0.   from this information i was able to find out that k is 16 and the mass is 1 slug. This would make the equation y''+16x=0, Knowing the de, should the equation be     c1cosew(t)+c2sinw(t) which would yield c1cos16t+c2sin16t. Would this be my equation of motion? Also do I take the square root of 16? Now I know x'(0)=0 and x(0)=1 , this is where i get confused in finding my c1 and c2 values. I think c2=0 and c1=1 , so knowing this, my equation of motion would be        x(t)=cos16t?  than to find the period, I would than use the formula 2pi/w=2pi/16=pi/8? than pi/8 would be my period. However if all of this is correct, how would i go about finding my amplitude? For the complete cycles in 4pi seconds, it would be the frequency, if so than frequency=1/period. Which yields 8/pi. but how do i use the 4pi?? If someone could justify my work and logics and offer any information to help me finish the problem, that would be excellent.

Also, this wouldn't be a damped or driven force would it? I am thinking it should be simple harmonic. Also is there a way to verify my answers through maple? That is not a huge deal as long as I am on track and everything looks good.