(Solved): Interpolation with Systems of Linear Equations. An object is initially attached to a spring. Then, ...

Interpolation with Systems of Linear Equations. An object is initially attached to a spring. Then, the object is allowed to reach an equilibrium position, in which it remains static. After inducing a perturbation, the position of the object changes with respect to time, as shown in the following table. Problem 4.1. Use MATLAB to determine the position of the object when $t=18\mathrm{s}$. Consider a $2^{\text{nd }}$-order interpolating polynomial and the method of linear equations. Then, show in a single plot an overlay of the raw data, the interpolating polynomial covering the full range of times, and the estimated position at $t=18\mathrm{s}$. Problem 4.2. Use MATLAB to determine the position of the object when $t=18\mathrm{s}$. Consider a $3^{\text{rd }}$-order interpolating polynomial and the method of linear equations. Then, show in a single plot an overlay of the raw data, the interpolating polynomial covering the full range of times, and the estimated position at $t=18\mathrm{s}$. Problem 4.3. Use MATLAB to determine the position of the object when $t=18\mathrm{s}$. Consider a $7^{\text{th }}$-order interpolating polynomial and the method of linear equations. Then, show in a single plot an overlay of the raw data, the interpolating polynomial covering the full range of times, and the estimated position at $t=18\mathrm{s}$. Problem 4.4. Calculate the true percentage errors of the estimates generated in problems $4\mathrm{a},4\mathrm{b}$, and $4\mathrm{c}$, if the true position of the object is $P=0.15\mathrm{cm}$ at $t=18\mathrm{s}$.