A particle is subjected to two S H Ms x₁ = A₁ sin wt and x₂ = A₂ sin (wt + $large frac{pi }{4}$ ). The resultant S H M will have an amplitude of

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$large frac{{{A_1} + {A_2}}}{2}$

$large sqrt {A_1^2 + A_2^2}$

$large sqrt {A_1^2 + A_2^2 + sqrt 2 {A_1}{A_2}}$

A₁A₂

answer is C.

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Detailed Solution

$large {A_{net}}, = ,sqrt {A_1^2 + A_2^2 + 2{A_1}{A_2}cos phi }$

$large phi rightarrow$ Phase angle between two S.H.M waves

$large phi , = ,frac{pi }{4}$

$large {A_{net}}, = ,sqrt {A_1^2 + A_2^2 + 2.{A_1}{A_2} times cos left( {frac{pi }{4}} right)}$

$large , = ,sqrt {A_1^2 + A_2^2 + 2.{A_1}{A_2} times frac{1}{{sqrt 2 }}}$

$large , = ,sqrt {A_1^2 + A_2^2 + sqrt 2 .{A_1}{A_2}}$

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