Question

2. Investigate resonance for the following differential equation $9x'' + 6x' + 37x = cos(\omega t)$. First evaluate the parameters $k_0$, $\tau_0$, $\omega_0$, $B_0$ exactly and then $Q$ approximately (2 decimal places) and then use calculus plus the formula for the response amplitude \begin{equation} A(\omega) = B_0 \left( (\omega^2 - \omega_0^2)^2 + k_0^2 \omega^2 \right)^{-\frac{1}{2}} , \end{equation} to find the exact and 4 decimal place approximations for the peak frequence $\omega_{peak}$ and amplitude $A(\omega_{peak})$ and do the same for the natural freqency $\omega_0$ and amplitude. [Be sure to show your calculus steps and evaluation details by hand.] \begin{equation} \text{Compare the value of the ratio } \frac{A(\omega_{peak})}{A(0)} \text{ with } Q. \text{ Finally evaluate and plot the ratio } \frac{A(\omega)}{A(0)} \text{ versus the frequency for } 0 \le \omega \le 10 \text{ with the gridline option on. [plot 3]} \end{equation}

          2. Investigate resonance for the following differential equation $9x'' + 6x' + 37x = cos(\omega t)$. First evaluate the parameters $k_0$, $\tau_0$, $\omega_0$, $B_0$ exactly and then $Q$ approximately (2 decimal places) and then use calculus plus the formula for the response amplitude \begin{equation*} A(\omega) = B_0 \left( (\omega^2 - \omega_0^2)^2 + k_0^2 \omega^2 \right)^{-\frac{1}{2}} , \end{equation*} to find the exact and 4 decimal place approximations for the peak frequence $\omega_{peak}$ and amplitude $A(\omega_{peak})$ and do the same for the natural freqency $\omega_0$ and amplitude. [Be sure to show your calculus steps and evaluation details by hand.] \begin{equation*} \text{Compare the value of the ratio } \frac{A(\omega_{peak})}{A(0)} \text{ with } Q. \text{ Finally evaluate and plot the ratio } \frac{A(\omega)}{A(0)} \text{ versus the frequency for } 0 \le \omega \le 10 \text{ with the gridline option on. [plot 3]} \end{equation*}

2. Investigate resonance for the following differential equation 9x” + 6x' + 37x = cos(ω t). First evaluate the parameters k0, τ0, ω0, B0 exactly and then Q approximately (2 decimal places) and then use calculus plus the formula for the response amplitude
A(ω) = B0 ( (ω^2 - ω0^2)^2 + k0^2 ω^2 )^-(1)/(2) ,
to find the exact and 4 decimal place approximations for the peak frequence ωpeak and amplitude A(ωpeak) and do the same for the natural freqency ω0 and amplitude. [Be sure to show your calculus steps and evaluation details by hand.]
Compare the value of the ratio (A(ωpeak))/(A(0)) with Q. Finally evaluate and plot the ratio (A(ω))/(A(0)) versus the frequency for 0 ≤ω≤ 10 with the gridline option on. [plot 3]

Added by Jessica B.

Question

Please give Ace some feedback