A. Write down an algebraic expression and make a correct graph (not just a sketch) for the velocity of your mass as function of time. Attach the graph with your answer. Explain and show the intermediate steps of how you arrived at your answer. HINT: This is a multistep process which will require you to figure out what trigonometric function best describes the situation, figuring out its correct argument, phase, and amplitude. B. Write down an algebraic expression and make a correct graph (not just a sketch) for the position of your mass as function of time. Attach the graph with your answer. Explain and show the intermediate steps of how you arrived at your answer. HINT: There are many ways to approach this part. You can use your velocity vs. time graph as a starting point to figure out the correct trigonometric function for your position. For the amplitude of your function, you can either use dimensional analysis or conservation of energy. C. Write down an algebraic expression and make a correct graph (not just a sketch) for the acceleration of your mass as function of time. Attach the graph with your answer. Explain and show the intermediate steps of how you arrived at your answer. HINT: There are many ways to approach this part. You can use either your velocity or position vs. time graph as a starting point to figure out the correct trigonometric function for your acceleration. For the amplitude of your function, you can either use dimensional analysis or Newton's laws. D. Write down an algebraic expression and make a correct graph (not just a sketch) for the kinetic energy of your mass as function of time. Attach the graph with your answer. Explain and show the intermediate steps of how you arrived at your answer. E. Write down an algebraic expression and make a correct graph (not just a sketch) for the potential energy of your mass as function of time. Attach the graph with your answer. Explain and show the intermediate steps of how you arrived at your answer. F. The kinetic and potential energy curves oscillate, but not about zero. They also seem to oscillate twice as fast as the velocity or position curves. Is this correct? Explain. G. Write down an algebraic expression and make a correct graph (not just a sketch) for the total energy of your mass as function of time. Attach the graph with your answer. Simplify your answer as much as possible. Explain and show the intermediate steps of how you arrived at your answer. Does your answer seem consistent with the principles of conservation of energy? Explain.

Consider our simplest model of a horizontal object mass m=200g attached to a spring of stiffness k=2N/m. k I'll\"!!- Let's start with our usual assumptions of no frictional forces anywhere and the spring being massless and obeying Hook's law in the entire range of motion. We place the origin of our coordinate system at the equilibrium position of the spring with the positive direction of the horizontal x-axis pointing to the left (towards the wall). You started your clock right at the moment when the mass was passing through the equilibrium position moving to the right (away from the wall) with the speed v=1m/s