33.65 ... Consider two vibrations of equal amplitude and frequency but differing in phase, one along the 12 x-axis,
x = a sin (wt - α)
and the other along the
y = a sin (wt - b)
These can be written as follows:
x/a = sin wt cos ∝ - cos wt sin ∝ (1)
y/a = sin wt cos β - cos wt sin β (2)
(a) Multiply Eq. (1) by sin b and Eq. (2) by sin a, and then subtract the resulting equations. (b) Multiply Eq. (1) by cos b and The following data give the amount Eq. (2) by cos a, and then subtract the resulting equations. ids over a path length of 100 cm: (c) Square and add the results of parts (a) and (b). (d) Derive the equation x 2 + y2 - 2xy cos d = a2 sin2 d, where d = a - b.lutamic Concentration acid (g/100 mL) (e) Use the above result to justify each of the diagrams in Fig. P33.65. In the figure, the angle given is the phase difference between two simple harmonic motions of the same frequency and amplitude, one horizontal (along the x-axis) and the other vertical (along the y-axis). The figure thus shows the resultant motion from the superposition of the two perpendicular harmonic motions.
