Chapter 14, Problem 25P

(III) A mass m is connected to two springs, with spring constants k₁ and k₂, in two different ways as shown in Fig. 14–32a and b. Show that the period for the configuration shown in part (a) is given by

$T=2\pi \sqrt{m\left(\frac{1}{k_1}+\frac{1}{k_2}\right)}$

and for that in part (b) is given by

$T=2\pi \sqrt{\frac{m}{k_1+k_2}}.$

Ignore friction.