Al-Shaghay, Yasmine T. Introduction to Physics PHYC1290 Due Fri, Jan 23, 2015 at

Question

Al-Shaghay, Yasmine T. Introduction to Physics PHYC1290 Due Fri, Jan 23, 2015 at 23:59 ends and s Assignment 2 times gre ID 3121 frequency waves." This type of problem was used in a previous fina by(z, t The two graphs below show the shape of two slinkies, a and ue noo of the sec See p.594 in your textbook, "The mathematics of stand- See p.594 in y 9. [1p ing etam. of problem wus used in e previous final , a and meters, a three no 10. [1 any (non 11. [1 interfere 12. [1 that inte 13. [1 for 0 S zero spe b, at various times. Given that the transverse displacement 10. of each slinky never exceeds 40 cm, answer the following ques- tions. 0.4 0.37 0.2 0.2 Use eramin ·0.3 0.3t.· · Pr--k-+- h-...: 14. select t For exa satisfie 3, 4 ar motion A) 1 0.4 sos 0.2 0.1 x (m B) 0.1 C) 2 0.2 E) F) G) H) 1. [1pt] A mathematical formula for the motion of slinky (b) is y = A cos(kr+0) cos(wt). If t2 = 1.50 s and 20 = 3.90 m, then find . N

Explanation / Answer

Answer 1)

y = Acos(kx + p)cos(wt)
assume p stands for phi in question.

At t=t2,
y = 0.1 m
xo = 3.90 m
so each division on x-scale corresponds to 3.90/25 = 0.156 m

At t = t2, x = 0.156*6 = 0.936 m

Time period T = 2t4 seconds
and t4 = 8t2 = 16s
So, T = 32 s
T = 2pi/w
or w = 2*3.14/32
= 0.19625 s-1

So. y = Acos(kx + p)cos(wt)
or 0.1 = 0.4*cos(k0.936 + p)cos(0.19625*1.50)
or 0.25 = cos(0.936k + p)*0.99
or 0.936k + p = 75.37
or p = 75.37 - 0.936k (ans)

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