Question

Help with part c please!

The equation h = 7 cos (pi/3 t) models the height h in centimeters after t seconds of a weight attached to the end of a spring that has been stretched and then released.

a. Solve the equation for t.
b. Find the times at which the weight is first at a height of 1 cm, of 3 cm, and of 5 cm above the rest position. Round your answers to the nearest hundredth.
c. Find the times at which the weight is at a height of 1 cm, of 3 cm, and of 5 cm below the rest position for the second time. Round your answers to the nearest hundredth.

Answer 1

I got part a and b already, the equation for part a is t=3arccos(h/7)/pi
Help with part c please! @Mertsj

Answer 2

@satellite73 @jim_thompson5910 @Hero @phi @campbell_st

Answer 3

@robtobey @mathstudent55 @hba

Answer 4

replace h with the given heights.
make sure you are in radian mode when you do the arc cosine

Answer 5

you can type
plot y=7 cos (t*pi/3)
into google to see a graph

Answer 6

Do I do the same thing as in part b but make the number neagtive or something?

Answer 7

remember that the period is 2pi/T = pi/3 so T= 6 seconds
the second cycle starts 6 seconds in

Answer 8

In b I basically plugged in for h into my equation to find the answers, c looks like almost the same problem except for it starts below not above, what difference does that make for my problem?

Answer 9

for (c) I think you use negative numbers for the distance, but you must add 6 seconds to account for it being for the second time

Answer 10

using the graph from google, you can see -1 cm occurs the 2nd time around at about 7.6 seconds

Answer 11

although there is some ambiguity .... the height is at -1 the first time at 1.6 seconds,
and then at 4.3 seconds (on the way back up), and then at 7.6 seconds during the 2nd cycle.

I assumed **below the rest position for the second time.** meant the 2nd cycle, but who knows?

Answer 12

Basically what I got from this is that I can plug the numbers 1, 3, and 5 cm into my equation as negatives, and I add 6 seconds as a result of it being in the second cycle?

Answer 13

@phi

Answer 14

yes, I think so.

Answer 15

Thanks