Question

Find a model for simple harmonic motion if the position at t = 0 is 2, the amplitude is 2 centimeters, and the period is 6 seconds.

Answer 1

A

Answer 2

B

Answer 3

C

Answer 4

D

Answer 5

Do you have any idea how to start this? For example, do you know what is the amplitude in each option?

Answer 6

no :(

Answer 7

i need alot of help

Answer 8

They have told you that the ordered pair (0,2) is on the graph.

Answer 9

In the first choice, you have 6sin(2t)

Answer 10

yes (:

Answer 11

Replace t with 0 and evaluate. Do you get 2?

Answer 12

So, a simple harmonic motion (or wave) has the following form.\[d = A \cos(\frac{2π}{T}t+k) = A \cos(ωt+k)\]
or \[d = A \sin(\frac{2π}{T}t+k) = A \cos(ωt+k)\]
where A is the amplitude, T is the period and ω is the angular frequency. So from the formula above, what do you think is the amplitude for the choice A?

Answer 13

Forgot to mention that k is the initial phase of the harmoniv motion.

Answer 14

no i get 0

Answer 15

Then move on to the next option. Replace t with 0 and see if you get 2.

Answer 16

for b i got square root of 3 if i plug it in.

Answer 17

So move on to the next choice.

Answer 18

for c i got -1

Answer 19

Actually, in the second choice, you get 0 again because pi/3 times 0 is 0 and the sin of 0 is 0

Answer 20

Are you remembering that anything times 0 is 0?

Answer 21

for D i got like 1.9

Answer 22

and yeah i do remember.

Answer 23

D: 2 cos(6t)

Answer 24

What is 6 times 0 ?

Answer 25

0

Answer 26

What is the cosine of 0 ?

Answer 27

1

Answer 28

What is 2 times 1 ?

Answer 29

2

Answer 30

Now explain to me again how you got 1.9 for D ?

Answer 31

http://www.wolframalpha.com/input/?i=2cos%2812%29