A light spring with spring constant k1 hangs from an elevated support. From its

Question

A light spring with spring constant k1 hangs from an elevated support. From its lower end hangs a second light spring, which has spring constant k2. An object of mass m is hung at rest from the lower end of the second spring.
(a) Find the total extension distance of the pair of springs. (Use any variable or symbol stated above along with the following as necessary: g for gravitational acceleration.)
xtotal =

(b) Find the effective spring constant of the pair of springs as a system. We describe these springs as in series. (Use any variable or symbol stated above as necessary.)
ktotal =

Explanation / Answer

(a)
The total extension X = x1 + x2
The force devloped in each spring is
F = - k1 x1 = - k2 x2
==> x1 = - F/k1, and x2 = - F/ k2
Therefore  X = -F / k1 - F/k2
                       = - F * [k1 + k2] / [k1*k2]
(b) The effective spring constant of the system is
K total = - {k1*k2 / [k1 + k2] }

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