It will be very much appreciated if you answer the part A, B, C, D, and E with e

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It will be very much appreciated if you answer the part A, B, C, D, and E with explanation.

Thanks.

Consider two vibrates of equal amplitude and frequency but differing in phase, one along the x-axis, and the other along the y-axis These can be written as follows: (a) Multiply Eq. (1) by sin beta and Eq. (2) by sin alpha, and then subtract the resulting equations, (b) Multiply Eq. (1) by cos beta and Eq. (2) by cos alpha, and then subtract the resulting equations, (c) Square and add the results of parts (a) and (b). (d) Derive the equation x2 + y2 - 2xycosdelta = a2 sin2 delta, where delta = alpha - beta. (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. Figure P33.65

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