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>> $The displacement equations of two simple$

Question

The displacement equations of two simple harmonic oscillators are given by $x_{1} = A_{1} cos ω t$ ; $x_{2} = A_{2} sin (ω t + \frac{π}{6})$ . The phase difference between them is:

A

$3 0^{\circ}$

B

$6 0^{\circ}$

C

$9 0^{\circ}$

D

$12 0^{\circ}$

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Updated on : 2022-09-05

Solution

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Correct option is B)

$X_{1} = A_{1} c o s ω t = A_{1} s i n (ω t +^{π} /_{2})$
$X_{2} = A_{2} s i n (ω t +^{π} /_{6})$
so, phase difference $= \frac{π}{2} - \frac{π}{6} = \frac{π}{3} = 6 0^{0}$

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