Step 1:

The curve equation is $\"\"$ and interval of the graph is $\"\"$ .

The damped vibration curve is in the form of $\"\"$ , where $\"\"$ .

Here $\"\"$ determines the path of the motion of particle.

Compare the above equation with general form of damped curve equation.

$\"\"$ determines the path of the motion of the curve.

Construct a table for different values of $\"\"$ .

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

$\"\"$	$\"\"$	$\"\"$	$\"\"$	$\"\"$	$\"\"$	$\"\"$	$\"\"$
$\"\"$	$\"\"$	$\"\"$	$\"\"$	$\"\"$	$\"\"$	$\"\"$	$\"\"$

Graph:

(1) Draw the coordinate plane.

(2) Plot all the points obtained in the table.

(3) Plot the path of curve.

(3) Connect all the points to a smooth curve.

$\"\"$

Solution:

The graph of the curve is

$\"\"$