Using an eccentric mass shaker, a dynamic test was run on a structure in which the exciting frequency was varied over a range of values. For each frequency, the response amplitude as well as the phase angle were measured and the following data was obtained. The estimated natural frequency of the structure is [latex]2 \mathrm{~Hz}[/latex]. Plot a frequency versus amplitude curve; then using the half power method, obtain an estimate of the damping. It will be readily seen that the graphical relationship obtained by taking the amplitude [latex]\rho[/latex] and the phase angle [latex]\phi[/latex] as polar coordinates is a Nyquist plot. Draw such a plot from the data supplied. By estimating the values of [latex]\Omega_1[/latex] and [latex]\Omega_2[/latex] corresponding to [latex]\phi=45^{\circ}[/latex] and [latex]135^{\circ}[/latex] from the Nyquist plot, obtain an estimate of the damping. Of the two estimates of damping obtained by you, which do you think is more reliable. [latex]\begin{array}{lrr}\Omega(\mathrm{Hz}) & \rho(\mathrm{mm}) & \phi(\mathrm{deg}) \\ 0.0 & 5.00 & 0.0 \\ 0.4 & 5.20 & 2.4 \\ 0.8 & 5.60 & 5.4 \\ 1.2 & 7.70 & 10.6 \\ 1.6 & 12.70 & 24.0 \\ 1.8 & 19.10 & 43.5 \\ 2.0 & 25.00 & 90.0 \\ 2.2 & 16.40 & 133.2 \\ 2.4 & 10.00 & 151.4 \\ 2.8 & 5.00 & 163.7 \\ 3.2 & 3.10 & 168.4 \\ 3.6 & 2.20 & 170.9 \\ 4.0 & 1.70 & 172.4\end{array}[/latex]

Question 6.P.14: Using an eccentric mass shaker, a dynamic test was run on a ...

Using an eccentric mass shaker, a dynamic test was run on a structure in which the exciting frequency was varied over a range of values. For each frequency, the response amplitude as well as the phase angle were measured and the following data was obtained. The estimated natural frequency of the structure is $2 \mathrm{~Hz}$ . Plot a frequency versus amplitude curve; then using the half power method, obtain an estimate of the damping.

It will be readily seen that the graphical relationship obtained by taking the amplitude $\rho$ and the phase angle $\phi$ as polar coordinates is a Nyquist plot. Draw such a plot from the data supplied. By estimating the values of $\Omega_1$ and $\Omega_2$ corresponding to $\phi=45^{\circ}$ and $135^{\circ}$ from the Nyquist plot, obtain an estimate of the damping.

Of the two estimates of damping obtained by you, which do you think is more reliable.

$\begin{array}{lrr}\Omega(\mathrm{Hz}) & \rho(\mathrm{mm}) & \phi(\mathrm{deg}) \\ 0.0 & 5.00 & 0.0 \\ 0.4 & 5.20 & 2.4 \\ 0.8 & 5.60 & 5.4 \\ 1.2 & 7.70 & 10.6 \\ 1.6 & 12.70 & 24.0 \\ 1.8 & 19.10 & 43.5 \\ 2.0 & 25.00 & 90.0 \\ 2.2 & 16.40 & 133.2 \\ 2.4 & 10.00 & 151.4 \\ 2.8 & 5.00 & 163.7 \\ 3.2 & 3.10 & 168.4 \\ 3.6 & 2.20 & 170.9 \\ 4.0 & 1.70 & 172.4\end{array}$

The blue check mark means that this solution has been answered and checked by an expert. This guarantees that the final answer is accurate.
Learn more on how we answer questions.