. Light, a textbook for students who have had one year of physics. Of 9 + y — B. cos fj. cos — -J- B sin 3. sin — (10) r t To find the equation of the path, we must eliminate, between(8) and (9) or between (8) and (10), that variable which hasno place in the simple equation of a line, viz., the time. Thiscan best be done by deriving from (8) 2tH- x L>-^ v x2 cos = and sin r= \ 1— A N A2 and substituting these values in ill) . This gives S. H AT RIGHT ANGLES 191 = — eos£ + B \1— -sin B A r * A2y— ^ cosp = B\jl — Ta m/3 Aa By squaring both sides, we get 2Bxy B2x2 2o T>2 . 2Q y2 — cos B
. Light, a textbook for students who have had one year of physics. Of 9 + y — B. cos fj. cos — -J- B sin 3. sin — (10) r t To find the equation of the path, we must eliminate, between(8) and (9) or between (8) and (10), that variable which hasno place in the simple equation of a line, viz., the time. Thiscan best be done by deriving from (8) 2tH- x L>-^ v x2 cos = and sin r= \ 1— A N A2 and substituting these values in ill) . This gives S. H AT RIGHT ANGLES 191 = — eos£ + B \1— -sin B A r * A2y— ^ cosp = B\jl — Ta m/3 Aa By squaring both sides, we get 2Bxy B2x2 2o T>2 . 2Q y2 — cos B i -rj cos2 B = BZ sin- /? B2x2 . sin2 jS ^, + ^.,=,./l x2 2xy x zxy . v A- ABt°S3+iF=Sin^ (U) Equation (11), represents an ellipse, except when sin 8 =0, that is, when the phase ditference 8 is either 0 or it. If8 = 0, cos g = 1, and the equation reduces to or, A2 AB^B* ^-^ = 0A B the equation of a straight line whose slope is 8 = — 1 and the equation reduces to If 6 = .+£= a straight line whose slope is — Figure 94 Figure 91 shows a number of typical shapes that the pathcan take according to the value of 8. In each case, the whole 192 LIGHT motion must lie within the rectangle of the dimensions 2A X215, for evidently x cannot be greater than -f A nor less than—-A. and y cannot be greater than +B nor less than — in the cases where the ellipse becomes a straight line,the path is tangent to the sides of the rectangle. Arrows showthe direction of motion in the path. The equation of theellipse cannot tell us anything about the direction of motion,for the time has been eliminated, but it can be determined foreach case by reasoning as in the following example: When/? = 7r/2, or 90°. the vertical motion must be % period behindthe horizontal, that is, y must be zero but increasing whenx --= -)- A. A quarter period later, y will be equal to -\- B,and x — 0. Since, in a quarter period, the point moves fromthe right-hand extr
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Keywords: ., bookcentury1900, bookdecade1920, booksubjectlight, bookyear1921
