$1.$ Create a set of input and output data $($preferably from a real system, such as a motor. Use the methods in $\backslash (4$: $5,11,12,13\backslash )$ to estimate the system and to analyze the accuracy of the estimation. $2.$ Measure uncertainties $($variances$)$ in the applied force and on the measurement. Also assign the sampling time. $3.$ Design a Kalman Filter to predict the displacement of the second mass. $4.$ Write Report and commentLeast Squares Estimation a$.$ Initial model structure selection $\backslash (4\mathrm{.}5\backslash )$ b$.$ Fitting parameterized model $\backslash (4\mathrm{.}6\backslash )$ c$.$ Fitting parameterized model Cost function $\backslash (4\mathrm{.}7\backslash )$ d$.$ Solving the linear least$-$squares ARX problem $\backslash (4\mathrm{.}8\backslash )$ Cost Function e$.$ Fitting parameterized model: Cost function $\backslash (4\mathrm{.}10\backslash )$ Toolbox Methods: Frequency response $\backslash (4\mathrm{.}11\backslash )2.$ Impulse response, residuals $\backslash (4\mathrm{.}12\backslash )3.$ Model validation using correlations $\backslash (4\mathrm{.}13\backslash )$