Solve for Ci using the method of Laplace transforms starting with the coupled differential equations given below. Show every detail of the calculation and reproduce formula (4). However instead of presenting this in the form given in formula (4), present it in terms of convolution.

A few hints:

1. Cp(t) is not given as an analytic function, it is in fact tabulated data below. When solving this system of equations, simply carry it as this symbol or its Laplace transform quantity Cp(s) when appropriate.

2. Use Cramer's Rule to solve for Ce(s) and Cm(s).

3. You may also want to use the quadratic formula to get some factors for a quadratic expression you get.

4. Remember how the convolution arises when applying the Laplace transform methodology, that is when you have a product of functions in s-space.

Differential Equations:

\f\f\f\f