Step 1:

The displacement of the bob of the pendulum is .

(a)

The displacement by an oscillating object from rest position at time is

.

Compare the equation with the above equation.

The equation represents the damped Motion of the object.

Here damping factor is

Mass of the object: .

Mass of the object is 40 kg.

(b)

Find Initial displacement of the bob.

Substitute in the displacement equation.

The negative sign indicates the displacement to the left of the resting position.

Initial displacement of the bob is .

(c)

 Graph the function .

Graph the and .

Note : the blue color in the graph indicates the motion of the function.

(d)

Find displacement at the start of second oscillation.

Time period of the function is .

Here

The second oscillation starts at .

Substitute in the displacement equation.

The negative sign indicates the displacement to the left of the resting position.

Displacement at the start of second oscillation is

(e)

Displacement of the bob as time increases without bound( t tends to infinity).

Displacement of the bob decreases and gets closer to 0 as time increases without bound.

Solution :