Duration: 6:07

26 views

0

Equations of displacements during three different SHMs of a particle can be written as \( x_{1}=A_{1} \cos \omega, t_{1}, x_{2}= \) \( A_{2} \cos \left(\omega_{2} t+\delta_{2}\right) \) and \( y=A_{3} \cos \left(\omega_{3} t+\delta_{3}\right) \) here \( x_{1} \) and \( x_{2} \) are the displacement of the particle along \( x \)-axis during two
\( P \) different SHMs. \( y \) is the displacement of the particle

W during SHM along \( y \)-axis. \( x \) and \( y \) axis are orthogonal to each other.
Consider the super position of two SHMs along \( x \)-axis. The resultant displacement is \( \mathrm{x}=\mathrm{x}_{1}+\mathrm{x}_{2} \) and resultant amplitude is \( A=\left[A_{1}{ }^{2}+A_{2}{ }^{2}+2 A_{1} A_{2} \cos \left(\omega_{1}-\omega_{2}\right) t\right]^{1 / 2} \) if \( \omega_{1} \) \( \neq \omega_{2} \) and \( \delta_{2}=0 \).
Super position of two SHMs in perpendicular direction may result in SHM along a straight line or motion along a circle or an ellipse in clockwise or counter clockwise direction.
In superposition of two SHMs along mutually perpendicular directions. Identify the correct options
(A) If \( \omega_{1}=\omega_{3} \) and \( \delta_{3}=0 \) then the resulting motion is SHM with amplitude \( \sqrt{\mathrm{A}_{1}^{2}+\mathrm{A}_{3}^{2}} \) along line \( y=\frac{A_{3}}{A_{1}} x \)
(B) If \( \omega_{1}=\omega_{3}, \mathrm{~A}_{1}=\mathrm{A}_{3} \) and \( \delta_{3}=\frac{3 \pi}{2} \) then the resulting motion is a circular motion in counter clockwise direction.
(C) If \( \omega_{1}=\omega_{2}, A_{1} \neq A_{3} \) and \( \delta_{3}=\frac{\pi}{2} \) then the resulting motion is on elliptical path in clockwise direction
(D) If \( \omega_{1}=\omega_{3} \) and \( \delta_{3}=\pi \) then the resulting motion is on elliptical path in counter clockwise direction
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live