1. The problem statement, all variables and given/known data a bullet has mass=0.01kg velocity=150m/s, you have a cylinder with 5.0m^3 of air at STP with a piston at one end that has mass=0.1kg and surface area of 10cm^3 and is at rest. The bullet strikes and embeds itself into the piston. The system is to be considered adiabatic after the collision a)find the displacement of the piston b)what is the time period of oscillation of the piston 2. Relevant equations momentum, p=mv momentum of an inelastic collision= m1v1+m2v2= (m1+m2)V(final) kinetic energy of the system before collision=(1/2)[mass(bullet)][velocity(bullet)]^2 kinetic energy of the system after collision=(1/2)[mass(bullet)+mass(piston)][velocity(final)]^2 F=ma, F=kx time period of linear oscillation= 2(pi)sqrt([mass(bullet)+mass(piston)]/k) 3. The attempt at a solution I calculated the final velocity- V(final)=[0.1*150]/[0.1+0.01]= 13.63636363...m/s I calculated the kinetic energy before- (1/2)[0.1]^2=112.5 joules I calculated the kinetic energy after-(1/2)[0.1+0.01][13.636363...]^2=10.2272 joules Kinetic Energy lost=102.2728 joules <-this energy lost is imparted to the gas in the cylinder as heat(that is what we are told) I know that a=(kx)/m omega-w=sqrt(k/m) there for a=sqrt(k/m)[x/m] I know that the gas in the cylinder exerts a force on the piston and this force will slow the pistons movement till it stops and then the force will over come it and push the piston out till a "vacuum" force pulls the piston back in and thus the linear oscillation begins. I can't for the life of me figure out how to find "x" or "k" for that matter. The only other hint we were given is that air is to be considered diatomic for this problem and thus Cv=5/2 R and Cp=7/2 R thus gamma can be calculated as 7/5 but I don't know how this plays into it. Any insight would be helpful I have been staring at this and googling for at least 8 hours now.