Chapter 5.3, Problem 21E

To determine

To discuss: In the non-linear differential equation $m\frac{d^{2}x}{d{t}^2}+\beta \left|\frac{dx}{dt}\right|\frac{dx}{dt}+Kx=0$ the damping term is written as $\beta \left|\frac{dx}{dt}\right|\frac{dx}{dt}$ instead of $\beta {\left(\frac{dx}{dt}\right)}^2$.