InterviewSolution
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InterviewSolution
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Consider two simple harmonic motion along x and y-axis having same frequencies but different amplitudes as x = A sin (ωt + φ) (along x axis) and y = B sin ωt (along y axis).Then show that \(\frac{x^2}{A^2}\) + \(\frac{y^2}{B^2}\) -\(\frac{2xy}{AB}\)cos ϕ = sin2 ϕ and also discuss the special casesNote: when a particle is subjected to two simple harmonic motion at right angle to each other the particle may move along different paths. Such paths are called Lissajous figures. |
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Answer» (a) \(y = \frac{B}{A}x\) , equation is a straight line passing through origin with positive slope. (b) \(y = -\frac{B}{A}x\), equation is a straight line passing through origin with negative slope. (c) \(\frac{x^2}{A^2}\) + \(\frac{y^2}{B^2}\) = 1, equation is an ellipse whose center is origin. A2 B2 (d) \(x^2 + y^2 = A^2\) , equation is a circle whose center is origin. (e) \(\frac{x^2}{A^2}\) + \(\frac{y^2}{B^2}\) - \(\frac{2xy}{AB} \frac{1}{\sqrt{2}}\) = \(\frac{1}{2}\), equation is an ellipse which (oblique ellipse which means tilted ellipse) |
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