Question

Graph the damped vibration curve for 0 ≤ t ≤ 2π.

Answer 1

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.

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

Solution:

The graph of the damped vibration curve is