$5)(15$ points$)$

The following is the transfer function for a circuit, H$($j$)$:

H$($j$)=$

$$

$$

j

j

$$

$$

$5$

$2000.$

a$)$ Find an expression for the magnitude of H$($j$).$

b$)$ Find an expression for the phase of H$($j$).$

c$)$ Find an approximate expression for the circuit output in phasor form if the input were $100$

at $=2000.$ Be sure that this is a good approximation. Be sure to include both magnitude and

phase.

d$)$ Write the transfer function in terms of $$s$.$ That is$,$ find H$($s$)$