Question

Two simple harmonic motions are represented by the equations. y1 = 10 sin$\frac{\pi}{4}$ (12t + 1), y2 = 5(sin 3$\pi$t +$\sqrt{3}$cos 3$\pi$t) The ratio of their amplitudes is

• A. 1 : 1
• B. 1 : 3
• C. 3 : 2
• D. 2 : 3

Answer 1

Answer: (A)

1 : 1

Answer 2

Here, $y_{1} = 10\sin\frac{\pi}{4}(12t + 1)$

Or $y_{1} = 10\sin(3\pi t + \frac{\pi}{4})$ ……. (i)

And $y_{2} = 5(\sin 3\pi t + \sqrt{3}\cos 3\pi t)$

Or $= 10(\sin 3\pi t \times \frac{1}{2} + \cos 3\pi t \times \frac{\sqrt{3}}{2})$

$\Rightarrow$ $y_{2} = 10\sin(3\pi t + \frac{\pi}{3})$

Comparing equation (i) and (ii) with standard equation for SHM we get

$A_{1} = 10$ and $A_{2} = 10$ $\therefore\frac{A_{1}}{A_{2}} = \frac{10}{10} = \frac{1}{1}$