How to develop and simulate demodulation (by a secondorder PLL) of a single-tone FM wave

Develop a code to simulate demodulation (by a secondorder PLL) of a single-tone FM wave with 100kHz carrier (of unit amplitude) and a modulating wave.

m(t)=1/5*sin(2*pi*1000t)

For the output amplitudes of FM modulator (??) and VCO (??) equal unity, and for ?? = 10 and ?? = 20. Assume ?0 = ??.

Plot

(i) time-domain modulating signal

(ii) phase of transmitted signal,

(iii) phase detector output

(iv) recovered output signal for the initial 5 seconds.

Measure and compare the PLL lock-in time

Determine the maximum modulating frequency for which the PLL tracks the signal.