A spring/mass/dashpot system has mass 5 kg, damping constant 60 kg/sec and spring constant 605 kg/sec/sec. Express the ODE for the system in the form

$\displaystyle {x}{''}+{2}{p}{x}'+{\omega_{{0}}^{{2}}}{x}={0}$

Identify the natural (undamped) frequency of the spring:

$\displaystyle \omega_{{0}}$ = Preview Question 6 Part 1 of 3   (square Hz)

Identify the parameter $\displaystyle {p}$:

$\displaystyle {p}$ = Preview Question 6 Part 2 of 3   (Hz)

Now assume that the system has the oscillating forcing function $\displaystyle {\cos{{\left(\omega_{{0}}{t}\right)}}}$ with the same frequency as the spring's natural frequency. Complexify the ODE and use the real part as a particular solution:

$\displaystyle {x}{''}+{12}{x}'+{121}{x}={\cos{{\left(\omega_{{0}}{t}\right)}}}$

$\displaystyle {x}_{{p}}$ = Preview Question 6 Part 3 of 3   (meters)