Instantaneous Frequency

Consider the chirp signal

$$x(t)=\cos(2\pi(at^2+bt+\phi)).$$

1.

Determine values for a, b, and $\phi$, such that the instantaneous frequency of x(t) will start at 3800 Hz and end at 800 Hz over the time interval $0\leq t \leq 3$ seconds.

2.

Plot the instaneous frequency versus time over the interval $0\leq t \leq 3$ seconds.