please solve with matlab only!!

11. this problem is based on problem 32 in boyce & diprima, ... Your question has expired and been refunded. We were unable to find a Chegg Expert to answer your question. Question: Please Solve with MATLAB only!! 11. This problem is based on Problem 32 in Boyce & DiPrima, S... Please Solve with MATLAB only!! 11. 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 Hookes Law, but instead is of the form F = ?(ky + ?y3). If ? = 0, the assumption amounts to Hookes Law, but in this problem, we shall focus on ? ?= 0 (either positive or negative). If we have air resistance present with damping coefficient ?, then the equation of motion (assuming the displacement is indicated by the variable y) becomes my?? +?y? +ky+?y3 =0 (see Boyce & DiPrima, Problem 32 as above). Henceforth we shall normalize by assuming that m = k = 1 and ? = 0, and then take the initial conditions y(0) = 0, y?(0) = 0.

(a) Plot the solution when ? = 0. What is the amplitude and period of the solution?

(b) Let ? = 0.1. Plot a numerical solution. Is the motion periodic? Estimate the amplitude and period.

(c) Repeat part (b) for ? = 0.2, and then for ? = 0.3.

(d) Plot your estimated values of the amplitude A and period T as functions of ?. How do A and T depend on ??

(e) Repeat parts (b)(d) for negative values of ?.