Question

Two mutually perpendicular SHM are represented by the equation x=4sin2pift
y=3cos2pift
Find the semi major and semi minor axis of an ellipse formed by their super position

Answer 1

Answer:Let’s assume that two independent forces acting on a particle in such a manner that the first alone produces a simple harmonic motion in the x- direction givenby

=

and the second would produce a simple harmonic motion in the y-direction given by

= +

Thus, we are actually considering the superposition of two mutually perpendicular SHMs which have equal frequencies. The amplitudes are different and their phases differ by. The resultant motion of the particle is a combination of the twoSHMs.

The position of the particle at any time t is given by (x, y) where x and y are given by the above equations. The resultant motion is, thus, two-dimensional and the path of the particle is, in general, an ellipse. The equation of the path traced by the particle is obtained by eliminating t from above equations

Now,

= and =1−

Putting these values in equation for y,

= += +1−

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