Answer to Question #88736 in Electricity and Magnetism for Shivam Nishad

Question

Two mutually perpendicular oscillations
have angular frequency o)0 and amplitudes
al and a2 such that al > a2. If the initial
phase difference between these is 4),
determine the nature of the resultant
oscillation obtained on their superposition.

Answer 1

The equation of the resultant path is given by formula

$$\frac {x^2} {a_1 ^2} + \frac {y^2} {a_2 ^2} – 2 \frac {xy} {a_1 a_2} \cos \phi = \sin^2 \phi (1)$$

In our case,

$$\phi=4\pi$$

Using (1) we got:

$$\frac {x^2} {a_1 ^2} + \frac {y^2} {a_2 ^2} – 2 \frac {xy} {a_1 a_2} = 0$$

Answer:

$$\frac {x^2} {a_1 ^2} + \frac {y^2} {a_2 ^2} – 2 \frac {xy} {a_1 a_2} = 0$$