1. The problem statement, all variables and given/known data A 1.15-kg mass oscillates according to the equation x = .650cos(8.40t) where x is in meters and t in seconds. Determine a)the amplitude, b)the frequency, c) the total energy of the system, and d) the kinetic and potential energy when x = 0.360m. 2. Relevant equations x = Acosωt ω = 2πf Etotal = KE + PEs +PEg = 1/2mv² + 1/2kx² + mgy v = rω ∑F = ma F = kx 3. The attempt at a solution a) Amplitude is given in the problem. A = .650m b) Frequency f = ω/2π = 8.40/2π = 13.2 Hz c) Total Energy E = 1/2mv² + 1/2kx² + mgy This is where I am having difficulty, and feel like I am taking a complicated route and overlooking a simple solution. I assume there is no gravitational potential energy, since the problem doesn't mention any change in height. Simplifying and manipulating the equation for total energy I get the following: E = 1/2m(Aω)² + 1/2(mg/x)(x²) = 1/2m[(Aω)² + gx] E = 1/2(1.15)[(8.40*0.650)² + 9.8*0.360] = 19.2 J I don't think this is correct, since I'm pretty sure I'm not supposed to use x = 0.360 in the equation. If I use the equation given in the problem I'd need to know t. I don't think this is the right way of going about this problem. I know I am not thinking about this correctly, and all of the possible equations and different forms are muddling my thought process. Can I just calculate the total energy at ANY position to make this simpler? If so, I would use the equilibrium position x = 0, and my equation would be E = 1/2m(Aω)² = 17.14 J.