3.7 Two springs having stiffness

k_(1)

and

k_(2)

, respectively, are used in a vertical position to support a single object of mass

m

. Show that the angular frequency of oscillation is

[(k_(1)+k_(2))/(m)]^((1)/(2))

if the springs are tied in parallel, and

[k_(1)(k_(2))/(k_(1)+k_(2))m]^((1)/(2))

if the springs are tied in series.

Two springs having stiffness k1 and k2, respectively, are used in a vertical position to support a single object of mass m. Show that the angular frequency of oscillation is [(k1+k2)/m]1/2 if the springs are tied in parallel, and [k1k2/(k1+k2)m]1/2 if the springs are tied in series