SATHEE: Simple Harmonic Motion 5 Question 12

Simple Harmonic Motion 5 Question 12

17. Two simple harmonic motions are represented by the equations $y_{1} = 10 \sin (3 π t + π / 4)$ and $y_{2} = 5 (\sin 3 π t + \sqrt{3} \cos 3 π t)$ . Their amplitudes are in the ratio of …… .

$(1986, 2 M)$

Match the Columns

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Answer:

Correct Answer: 17. $1 : 1$

Solution:

$A_{1} = 10$ (directly)

For $A_{2} : y_{2} = 5 \sin 3 π t + 5 \sqrt{3} \cos 3 π t$

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

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

$\begin{aligned} A_{2} & = \sqrt{(5)^{2} + (5 \sqrt{3})^{2}} = 10 \\ ∴ & \frac{A_{1}}{A_{2}} & = \frac{10}{10} = 1 \end{aligned}$

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Simple Harmonic Motion 5 Question 12

17. Two simple harmonic motions are represented by the equations y1=10sin⁡(3πt+π/4) and y2=5(sin⁡3πt+3cos⁡3πt). Their amplitudes are in the ratio of …… .

Match the Columns

Answer:

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17. Two simple harmonic motions are represented by the equations $y_{1} = 10 \sin (3 π t + π / 4)$ and $y_{2} = 5 (\sin 3 π t + \sqrt{3} \cos 3 π t)$ . Their amplitudes are in the ratio of …… .