Chapter 2, Problem 19P

The equivalent stiffness of a series-parallel combination of three springs shown in Fig. P2.19 is given by

$k=k_2+\frac{k_1{k}_2}{k_1+k_2}$ (2.65)

If $k_1=k_2+2$ lb/in and the equivalent stiffness is $k=1.75$ lb/in, find $k_1$ and $k_2$ as follows:

(a) Substitute the values of k and $k_1$ into equation (2.65) and obtain the quadratic equation for $k_2$. (b) Using the method of your choice, solve the quadratic equation obtain in part (a) and determine the values of $k_2$. Also, find the values of $k_1$.