PHY 5346
Homework Set 12 Solutions – Kimel
2. 7.1 I shall apply Eqs.(26), (27), and (28)
s0 + s1
2
= a1
s0 − s1
2
= a2
δ l = δ2 − δ1 = sin−1
s3
2a1a2
s0 + s3
2
= a+
s0 − s3
2
= a−
δc = δ− − δ+ = sin−1
s2
2a+a−
a) s0 = 3, s1 = −1, s2 = 2, s3 = −2
a1 = 1, a2 = 2
δ l = sin−1
−2
2 2
= − 1
4
π rad
a+ = 1
2
, a− =
5
2
δc = sin−1
2
2
1
2
5
2
= 1. 1071 rad
b) s0 = 25, s1 = 0, s2 = 24, s3 = 7
a1 =
25
2
, a2 =
25
2
δ l = sin−1
s3
2a1a2
= sin−1
7
2
25
2
25
2
= 0.283 79 rad
a+ =
32
2
= 4, a− =
s0 − s3
2
= 3
δc = δ− − δ+ = sin−1
24
24 × 3
= 1
2
π rad
To plot the two cases ReEx ≡ X = cosx, ReEy ≡ Y = rcoxx − δ l, where r = a2/a1 and x = ωt.
Case a) cosx,
2 cosx + π4
-1
-0.5
0.5
1
-1
-0.8 -0.6
-0.4 -0.2
0.2
0.4
0.6
0.8
1
Case b) cosx, cosx − 0.28379
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
-1
-0.8 -0.6
-0.4 -0.2
0.2
0.4
0.6
0.8
1