A spring with a weight attached is oscillating. The weight (which is attached at the bottom of the spring) is 5 feet from a 10-foot ceiling when it’s at rest. The motion of the weight can be described by the equation: y=3sin(pi*t - pi/2) , where y is the distance from the equilibrium point after time t (in seconds).

Question

a) Was the weight pulled down or pushed up before it was released?

b) How far was the weight from the ceiling when it was released?

c) How close will the weight come to the ceiling?

d) When does the weight first pass it’s equilibrium point?

e) What is the greatest distance that the weight will be from the ceiling?

f) Find the period of the motion. g) Find the amplitude of the motion.

h) What is the frequency of the motion?

i) How far from the ceiling is the weight after 2.5 seconds?

Answer 1

If you have no ideas on any of these questions, you seriously need to review your trig functions.

y = 5+3sin(πt-π/2) = 5+3sin(π(t-1/2))

(a) at t=0, y = 3sin(-π/2) = -3
Since that is below the equilibrium point, the weight was pulled down.

(b) all these distance from the ceiling questions can be answered by considering that the distance is just d = 5-y

(f) since the period of sin(kt) is 2π/k, we have a period of 2π/π = 2 seconds.

(g) the amplitude is clearly 3.

(h) f = 1/p

So, what do you get for the others, and how do you get it?