First slide

Simple hormonic motion

Question

A particle is subjected to two SHMs $x_{1} = A_{1} sinωt and x_{2} = A_{2} \sin (ωt + \frac{π}{4})$ . The resultant SHM will have an amplitude of

Easy

A

$\frac{A_{1} + A_{2}}{2}$
B

$\sqrt{A_{1}^{2} + A_{2}^{2}}$
C

$\sqrt{A_{1}^{2} + A_{2}^{2} + \sqrt{2} A_{1} A_{2}}$
D

$A_{1} A_{2}$

Solution

$A = \sqrt{A_{1}^{2} + A_{2}^{2} + 2 A_{1} A_{2} cosϕ}$

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