Question

The composition of two simple harmonic motions of equal periods at right angle to each other and with a phase difference of $\pi$ results in the displacement of the particle along

• A. Straight line
• B. Circle
• C. Ellipse
• D. Figure of eight

Answer 1

Answer: (A)

Straight line

Answer 2

If $y_{1} = a_{1}\sin\omega t$ and $y_{2} = a_{2}\sin(\omega t + \pi)$

⇒ $\frac{y_{1}}{a_{1}} + \frac{y_{2}}{a_{2}} = 0$⇒ $y_{2} = - \frac{a_{2}}{a_{1}}y_{1}$

This is the equation of straight line.