include matlab code please.

This problem is based on Problem 32 in Boyce & DiPrima, Section 3.7. Consider a frictionless mass-spring system as in Figure 3.7.10 in Boyce & DiPrima (standard mass attached to a spring on a frictionless table). Suppose the restoring force of the spring is not given by Hooke's Law, but instead is of the form F = -(ky + elementof u^3). If elementof = 0, the assumption amounts to Hooke's Law, but in this problem we shall focus on elementof notequalto 0 (either positive or negative). If we have air resistance present with damping coefficient gamma, then the equation of motion (assuming the displacement is indicated by the variable y) becomes my" + yy" + ky + elementof y^3 = 0 Henceforth we shall normalize by assuming that m = k = 1 and gamma = 0, and then take the initial conditions y (0) = 0, y' (0) = 0. (a) Plot the solution when elementof = 0. What is the amplitude and period of the solution? (b) Let elementof = 0.1. Plot a numerical solution. is the motion periodic? Estimate the amplitude and period. (c) Repeat pan (b) for elementof = 0.2, and then for elementof = 0.3. (d) Plot your estimated values of the amplitude A and period T as functions of elementof. How do A and T depend on elementof? (e) Repeat pans (b) - (d) for negative values of elementof. This problem is based on Problem 32 in Boyce & DiPrima, Section 3.7. Consider a frictionless mass-spring system as in Figure 3.7.10 in Boyce & DiPrima (standard mass attached to a spring on a frictionless table). Suppose the restoring force of the spring is not given by Hooke's Law, but instead is of the form F = -(ky + elementof u^3). If elementof = 0, the assumption amounts to Hooke's Law, but in this problem we shall focus on elementof notequalto 0 (either positive or negative). If we have air resistance present with damping coefficient gamma, then the equation of motion (assuming the displacement is indicated by the variable y) becomes my" + yy" + ky + elementof y^3 = 0 Henceforth we shall normalize by assuming that m = k = 1 and gamma = 0, and then take the initial conditions y (0) = 0, y' (0) = 0. (a) Plot the solution when elementof = 0. What is the amplitude and period of the solution? (b) Let elementof = 0.1. Plot a numerical solution. is the motion periodic? Estimate the amplitude and period. (c) Repeat pan (b) for elementof = 0.2, and then for elementof = 0.3. (d) Plot your estimated values of the amplitude A and period T as functions of elementof. How do A and T depend on elementof? (e) Repeat pans (b) - (d) for negative values of elementof