(Solved): 1. The equation of motion for the system shown in the figure is given as mx+cx+kx=cy(t)/2. ...

1. The equation of motion for the system shown in the figure is given as $$m\ddot{x}+c\stackrel{?}{x}+kx=c\stackrel{?}{y}(t)/2$$. (a) Find the complex frequency response $$G(j?)=\frac{?}{Y}$$ for $$y(t)=Y{e}^{j?t}$$, assuming $$x(t)=X{e}^{j?t}$$. (b) Write the amplitude of the frequency response $$?G(j?)?$$ in non-dimensional form, and calculate its value at resonance (when $$?={?}_n$$ ).