Question

Two simple harmonic motions are represented by

\(y_1 =10\,sin(4\pi t +\frac{\pi}{4})\)

y₂ = 5 (sin 3πt + √3 cos3πt)

The ratio of their amplitudes, and the magnitude of the phase difference between them, are, respectively,

(1) 1 and πt

(2) 2 and π(t - 1/12)

(3) 1 and π(t - 1/12)

(4) 2 and π(t)

Answer 1

(3) 1 and π(t - 1/12)

We first rewrite the equation for y₂ in the ‘standard form’. 

Let us put