Question

Two simple harmonic motions with the same frequency act on a particle at right angles i.e., along x and y axis. If the two amplitudes are equal and the phase difference is $\pi$ /2, the resultant motion will be :

• A. a circle
• B. an ellipse with the major axis along y-axis
• C. an ellipse with the major axis along x-axis
• D. a straight line inclined at 45? to the x-axis

Answer 1

Answer: (A)

The two simple harmonic motions can be given by $x=a\sin \omega t$ ?...(i) and $y=a\sin \left(\omega t+\frac{\pi }{2}\right)$ $y=a\cos \omega t$ ..?.(ii) On squaring and adding Eqs. (i) and (ii), we obtain $x^2+y^2=a^2({\sin }^2\omega t+{\cos }^2\omega t)$ or $x^2+y^2=a^2$ This is the equation of a circular motion with radius a. NOTE: Simple harmonic motion is of two types : 1. Linear simple harmonic motion 2. Angular simple harmonic motion