A dynamic system with input \(f\) and output \(\dot{x}\) is modeled as

\[\frac{3}{4} \ddot{x}+\dot{x}+k x=f(t), \quad k=\text { const }>0\]

a. Find the state-space form, and determine the value(s) of \(k\) for which the system is stable.

b. Find the transfer function directly from the state-space form.

c. Find the transfer function directly from the given model, and compare with (b).