(a) Write down Hooke's Law for the force of a spring on a mass as a function of (xx0), where x0 is the equilibrium position of the spring. (b) Where is the magnitude of the force maximized? Where is it minimized? (c) Derive an expression for the potential energy U stored in the spring as a function of its displacement. Sketch U(x). (d) What do you notice about the curvature of U(x), specifically in relation to your answers from (b)? (e) Using (a), derive an equation of motion for the spring in terms of x(t),x(t), and x(t). (f) Solve for x(t). (a) Write down Hooke's Law for the force of a spring on a mass as a function of (xx0), where x0 is the equilibrium position of the spring. (b) Where is the magnitude of the force maximized? Where is it minimized? (c) Derive an expression for the potential energy U stored in the spring as a function of its displacement. Sketch U(x). (d) What do you notice about the curvature of U(x), specifically in relation to your answers from (b)? (e) Using (a), derive an equation of motion for the spring in terms of x(t),x(t), and x(t). (f) Solve for x(t)