$14\mathrm{.}15$ Use arguments based on the phase angle in frequency

response to determine if the following combinations of

$G=G_v{G}_p{G}_m$ and $G_c$ become unstable for some value of $K_c.$

$($a$)G=\frac{1}{(4s+1)(2s+1)},G_c=K_c$

$($b$)G=\frac{1}{(4s+1)(2s+1)},G_c=K_c(1+\frac{1}{5s})$

$($c$)G=\frac{s+1}{(4s+1)(2s+1)},G_c=K_c\frac{(2s+1)}{s}$

$($d$)G=\frac{1-s}{(4s+1)(2s+1)},G_c=K_c$

$($e$)G=\frac{e^{-s}}{4s+1}$

$G_c=K_c$