An exponential decaying sinusoid has very interesting properties. In fluid dynamics, for example, the

following equation models the wave patterns of a particular liquid when it is perturbed by an external

force:

$y(x)=F{e}^{-ax}sin(bx)$

where $F$ is the magnitude of the external impulse force, and a and $b$ are constants associated with the

viscosity and density, respectively.

The following data have been collected for the following types of fluids:

write a function to obtain the wave patterns, $y(x)$ with a certain force, $F$ and the constants, $a$&$b$ for

a certain fluid, along with position vector, $x.($Thus the inputs are $F,a,b,$ and $x.)$ Name the function

as $fn\_$expdecay. You can assume that input value of $x$ is in radian.

Write a script that prompts the user for a value for $F,$a and $b.$ Input $($create$)$ an $x-$vector, and call the

function, $f{n}_{-}$expdecay to calculate y$-$vector. Also plot the wave pattern by using built$-$in function plot

with setting "blue solid line without marker". Name the script as WavePattern.

Plot the wave pattern for the above $3$ different fluids with $F=10.x$ points should be generated

between $-2$ and $2$ with step width of $0\mathrm{.}1.$ Copy&Paste the command window history as well as

plotting results into document file.