(a)

The equation of motion is .

Velocity is the derivative of position: .

.

Differentiate on each side with respect to .

Acceleration is the derivative of Velocity.

.

Differentiate on each side with respect to .

(b) Graph:

Graph the velocity and acceleration functions.

(c)

At the equilibrium position, .

Substitute  in the above expression.

Therefore at  sec , the mass pass through the equilibrium position.

(d)

After the equilibrium position mass travels maximum distance.

That is at the extreme travel distance the velocity is equals to zero.

Therefore we have,.

From the Pythagorean theorem:

 and  .

Substitute above values in  to find maximum distance.

Distance traveled by the mass after equilibrium position is 3.6 cm.

From the graph, it is clear that speed of the mass is maximum when .

Speed of the mass is greatest when 

(a)  and 

(b)

(c)

At  sec , the mass pass through the equilibrium position.

(d)

Distance traveled by the mass after equilibrium position is 3.6 cm.

(e)

Speed of the mass is greatest when