Graph displacement as function of time

[Gbox]

Homework Statement

let there be $\beta(t+\tau)^{-2}e^{-3}cos(at^{3})$ where $\beta$, $\tau$ and $a$ are constants

Homework Equations

$\beta(t+\tau)^{-2}e^{-3}cos(at^{3})$

The Attempt at a Solution

I know the graph is going up and down exponential but how can I draw it more accurately?

 

[RUber]

Find some benchmarks to plot...i.e. t = 0, $t^3 =$ some multiple of $\pi/a$.
Once you have some of those magnitudes and periods, you should have all you need.

 

[Gbox]

Find some benchmarks to plot...i.e. t = 0, $t^3 =$ some multiple of $\pi/a$.
Once you have some of those magnitudes and periods, you should have all you need.

I have a lot of constant so rather than at $t=0$ the answer says something like slope of about $\frac{1}{t^2}$ and frequency of about $t^3$ how did the get to it?

 

[RUber]

Change all your constants to 0 or 1 (whichever makes more sense), then look at the remaining function of t.
What is the frequency of cosine?