Simple Harmonic Motion 5 Question 12

17. Two simple harmonic motions are represented by the equations $\quad y _1=10 \sin (3 \pi t+\pi / 4) \quad$ and $y _2=5(\sin 3 \pi t+\sqrt{3} \cos 3 \pi t)$. Their amplitudes are in the ratio of …… .

$(1986,2 M)$

Match the Columns

Show Answer

Answer:

Correct Answer: 17. $1: 1$

Solution:

  1. $A _1=10$ (directly)

For $A _2: y _2=5 \sin 3 \pi t+5 \sqrt{3} \cos 3 \pi t$

$$ =5 \sin 3 \pi t+5 \sqrt{3} \sin 3 \pi t+\frac{\pi}{2} $$

i.e. phase difference between two functions is $\frac{\pi}{2}$, so the resultant amplitude $A _2$ can be obtained by the vector method as under

$$ \begin{aligned} & A _2 & =\sqrt{(5)^{2}+(5 \sqrt{3})^{2}}=10 \\ \therefore \quad & \frac{A _1}{A _2} & =\frac{10}{10}=1 \end{aligned} $$



NCERT Chapter Video Solution

Dual Pane