## ← 07-46 Period and Omega

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Showing Revision 1 created 07/23/2012 by Amara Bot.

1. Well, there is a couple of ways to answer this question,
2. at least a couple, and I'm going to show you too.
3. The period is 2 seconds and we're talking about 7.5 seconds.
4. If a mass starts off up here, what are 2 seconds is complete one period;
5. two more, it's gone up here; two more, another period.
6. Okay, so far we've had 6 seconds elapsed.
7. What are 7 seconds that's half a period, and then another half a second,
8. well that's another half of what's left.
9. We'd wind up here. How else could we have solve this?
10. Remember that the amount of angle we go through in a certain amount of time is equal to ω * t.
11. Okay, I know that t is 7.5 seconds. How can I find ω?
12. Well, we have this relationship, T = 2π/ω, or rearrange, ω = 2π/T.
13. In this case, with a T of 2, ω is equal to just π radians/sec.
14. That means in each second, it's going to go π radians.
15. Well, 7π radians would be seven-halves of the circle.
16. Starting from here, that would be this angle, one-half, two, three, four, five, six, and seven,
17. but it was 7.5 seconds, so the extra π over 2 radians, and again that puts us right here.