A block of mass \(m\) is suspended from the ceiling by a spring of stiffness \(k\). The equation of motion is

\[ m \ddot{x}+k x=0 \]

where \(x\) is measured from the static equilibrium position. Assume the initial conditions are \(x(0)=1\) in and \(\dot{x}(0)=1 \mathrm{in} / \mathrm{s}\). Solve for the response \(x(t)\) for two cases:

(a) the spring is assumed massless, and

(b) the mass of the spring is included.

Plot both solutions and comment on the importance of including the mass of the spring. Assume \(m g=1\) \(\mathrm{lb}\) and a spring mass that is \(10 \%\) of the block mass for \(k=0.1,1\), and \(10 \mathrm{lb} / \mathrm{in}\). What conclusions can be drawn?