Problem 1 Multiple problems in the real world will require the use of differential equations in order to describe the physical system that is being analyzed. In this case, we will focus on a mass-spring system that is being damped. Imagine that a block of mass m 4.2 kg is attached to a horizontal spring whose spring constant is k 378 kg/s2 and is being damped at a rate 31.5kg/s. The systern is in equilibrium, which means that no force is being applied F 0. We can describe the system using the following differential equation: where and z are the second and first derivatives of z with respect to time, respectively. (a) In order to find the solution to this differential equation we will find the two eigenvalues ni and n2. First, we will rewrite the equation in a quadratic form as follows , where n2 , n =, and z = 1 . Create a vector of cefficients and name it r (b) Using the roots0) function in MATLAB, find the roots for the quadratic equation. Your answer of a 2x1 vector; make sure to name it n. These are your eigenvalues. You will have to use the vector of coefficients in order to use the roots() function. You may have to look up in MATLAB what the roots0) function does and how to input the values into the roots) function. will come in a form of a 2x1 vector; make sure to name it n. T (c) Using indexing, create a new variable using the first eigenvalue and name it Pi. Create a second value using the second eigenvalue and name it pa (d) Your final solution can be expressed in the following form: Where Ci is a constant equal to 24.5 and C2 is equal to -24.5. Using the above equation, find the position of the block after 15 seconds has passed. Suppress all the variables for this part except for the final answer a