Physical Model

with

Parameter Identification

$m=$ pendulum mass $=1\mathrm{.}815kg$

$m_{\text{s}\text{p}\text{r}\text{i}\text{n}\text{g}}=$ spring mass $=0\mathrm{.}1445kg$

$=$ unstretched spring length $=0\mathrm{.}333m$

$k=$ spring constant $=172\mathrm{.}8\frac{N}{m}$

$g=$ acceleration due to gravity $=9$

$F_t=5\mathrm{.}71N=$ pre$-$tension of spring

$r_s=$ static spring stretch, i$.$e$.,r_s=(mg-F)k=0\mathrm{.}070m$

$r_d=$ dynamic spring stretch

$r=$ total spring stretch $=r_s+r_d$

Simulation of a physical system:

The physical model of the spring$-$pendulum system is:

$mr-m(l+r){}^{}{?}^2+kr+F_t-$mgcos$=0,$ Nonlinear Equations

Using the givenntmention of Motion

Matlab$/$Simulink simulation diagram to solve this mathematical mode

Simulate two sets of initial conditions shown in the next siles.

Submit the simulation diagrams and the plots of r vs$.t$ and $$ vs$.t$ for

each set of initial conditions. Discuss your results, especially focusing

on any discrepancies between the predicted dynamic behavior and the

actual dynamic behavior

Actual Measured Dynamic Behavior

Actual Measured Dynamic Behavior

Do a Simulink program