Chapter 8, Problem 35P

Real mechanical systems may involve the deflection of nonlinear springs. In Fig. P8.35, a mass m is released a distance h above a nonlinear spring. The resistance force F of the spring is given by

$F=-\left(k_{1}d+k_2{d}^{3/2}\right)$

Conservation of energy can be used to show that

$0=\frac{2k_2{d}^{5/2}}{5}+\frac{1}{2}{k}_1{d}^2-mgd-mgh$

Solve for d, given the following parameter values: $k_1=40,000\text{g}/{\text{s}}^2,k_2=40g/\left({\text{s}}^2{\text{m}}^{0.5}\right),m=95g,g=9.81\text{m}/{\text{s}}^2,\text{ and }h=0.43\text{m}$.

FIGURE P8.35