$4\mathrm{.}7$ System identification: Calculating $$ and ${}_n$ from

Shown right is the dynamic response $($time$-$history$)$ for an underdamped $2^{nd}-$order ODE.

Given this underdamped free vibration laboratory data, complete the general sequence of steps below to form numerical values for $$ and ${}_n$ and then determine values specific to the graph on the right.

Result:

$$~~$0\mathrm{.}15,{}_n$~~$3\mathrm{.}0\frac{\text{r}\text{a}\text{d}}{sec}$

Note: This procedure is motivated by Homework $4\mathrm{.}6.$

Mark the local maxima and$/$or minima and $y_{\text{e}\text{q}\text{u}\text{i}\text{l}\text{i}\text{b}\text{r}\text{i}\text{u}\text{n}}$

Mark the period $q,$ and get a better estimate of it by measuring $2**{}_{\text{p}\text{e}\text{r}\text{i}\text{o}\text{d}}$ and dividing by $2.$

Using the graph, estimate decayRatio.

Use that estimate of decayRatio and eqn$(6\mathrm{.}2)$ to calculate

Use that calculated value of $$ and eqn $(6\mathrm{.}3)$ to calculate $($damping ratio$).$

CS

$4\mathrm{.}7$ System identification: Calculating $$ and ${}_n$ from

Shown right is the dynamic response $($time$-$history$)$ for an underdamped $2^{nd}-$order ODE.

Given this underdamped free vibration laboratory data, complete the general sequence of steps below to form numerical values for $$ and ${}_n$ and then determine values specific to the graph on the right.

Result:

$$~~$0\mathrm{.}15,{}_n$~~$3\mathrm{.}0\frac{\text{r}\text{a}\text{d}}{sec}$

Note: This procedure is motivated by Homework $4\mathrm{.}6.$

Mark the local maxima and$/$or minima and $y_{\text{e}\text{q}\text{u}\text{i}\text{l}\text{i}\text{b}\text{r}\text{i}\text{u}\text{n}}$

Mark the period $q,$ and get a better estimate of it by measuring $2**{}_{\text{p}\text{e}\text{r}\text{i}\text{o}\text{d}}$ and dividing by $2.$

Using the graph, estimate decayRatio.

Use that estimate of decayRatio and eqn$(6\mathrm{.}2)$ to calculate

Use that calculated value of $$ and eqn $(6\mathrm{.}3)$ to calculate $($damping ratio$).$

CS