An object oscillates along a vertical line, and its position in centimeters is given by y(t) = 30 (sin t - 1), where t ≥ 0 is measured in seconds and y is positive in the upward direction.

a. Graph the position function, for 0 ≤ t ≤ 10.

b. Find the velocity of the oscillator, v(t) = y'(t).

c. Graph the velocity function, for 0 ≤ t ≤ 10.

d. At what times and positions is the velocity zero?

e. At what times and positions is the velocity a maximum?

f. The acceleration of the oscillator is a(t) = v'(t). Find and graph the acceleration function.