#1**+5 **

I think I can answer some of these.....

a. The spring will be at it's lowest point at 0 and 2pi seconds = -5 cm below the equilibrium point

It will be at it's highest point at pi seconds = +5 cm above the equilibrium point

b. The velocity is given by the derivative of the position function =

d ' (t) = v (t) = 5sin (t)

c. The speed will be greatest where the sine reaches its absolute maximum and minimum values, i.e., at t = pi/2 seconds and at 3pi/2 seconds......at both times the * speed* will be 5 cm/s

In the first case, the * velocity* will be +5cm/s and in the second, it will be -5cm/s

d. The acceleration is given by the derivative of the velocity function =

d '' (t) = v '(t) = a (t) = 5cos( t )

e. The acceleration = 0 at pi/2 seconds and at 3p/2 seconds since the cosine = 0 at these two values

CPhill
Feb 18, 2016