anonymous one year ago Can someone tell me these when an object moves in simple harmonic motion described by the equation d=4 cos(π/2 t + π/2) where t is measured in seconds and d in inches? https://i.imgur.com/7I5fMBj.jpg

1. dan815

springs have harmonic motion

2. dan815

period change too

3. dan815

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4. anonymous

a. $-1 \le cos(x) \le 1 \ so\ -4 \le 4.cos(x) \le 4$ b.c. $cos(x) \ cicle\ are \ 2\pi, \ \ \ 2\pi = t . \frac {\pi}{2} \, \ \rightarrow t = 4s$$freq = \frac{1}{t} \rightarrow freq = \frac {1}{4}$ d. shift left $\frac {\pi}{2}$ e. B

5. anonymous

So the maximum displacement of the object is 4 inches, the frequency is 2π cycles per second, the time required for one cycle is 4 seconds, and the phase shirt is π/2?

6. dan815

no

7. dan815

phase shift is 1 frequency= cycles/second if one cycle takes 4 secs then 1/4th cycle happens in 1 second

8. anonymous

Okay, then the maximum displacement of the object is still 4 inches, the frequency is now 1/4th cycles per second, the time required for one cycle is 4 seconds, and the phase shift is now 1 in.?