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Oscillations — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsOscillations3 Marks
Question
A particle is subjected to two simple harmonic motions in the same direction having equal amplitude and equal frequency. If the resultant amplitude is equal to the amplitude of individual motions, what is the phase difference between the motions?
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Answer

Here, $\text{a}_1=\text{r};\text{a}_2=\text{r}$ and $\text{R = r},\theta=?$ As $\text{R}^2=\text{a}^2_1+\text{a}^2_2+2\text{a}_1\text{a}_2\cos\theta$$\therefore\text{r}^2=\text{r}^2+\text{r}^2+2\text{r.r}\cos\theta$
$=2\text{r}^2(1+\cos\theta)$
$1+\cos\theta=\frac{1}{2}$
$\cos\theta=-\frac{1}{2},$
$=\cos120^{\circ}$
$\theta=120^{\circ}$
$=\frac{2\pi}{3}\text{radian}$

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