1a. For the system below, if the mass is pulled away from its equilibrium position as shown by x, then write what the force by the spring on the mass would be in vector notation and explain your reasoning. Take to the right to be the positive x direction. k1 m1 X 1b. Show that you get back the expected force by spring on mass from using F = -(dU/dx) on the spring potential energy U = (12) k x^2. 1c. Sketch the graph of U vs x. Explain why the graph looks as it does. 1d. List all resources consulted (names of people, spedific weblinks, books, articles, etc) or specify none.