A particle is subjected to two simple harmonic motions of the same frequency and direction. The amplitude of the first motion is `4.0 cm` and that of the second is `3.0 cm`. Find the resultant amplitude if the phase difference between the two motion is (a) `0^(@)` (b) `60^(@)` ( c) `90 ^(@)` (d) `180^(@)`

A particle is subjected to two simple harmonic motions of the same fre

1.	A particle is subjected to two simple harmonic motions of the same frequency and direction. The amplitude of the first motion is `4.0 cm` and that of the second is `3.0 cm`. Find the resultant amplitude if the phase difference between the two motion is (a) `0^(@)` (b) `60^(@)` ( c) `90 ^(@)` (d) `180^(@)`
Answer» Correct Answer - A::B::C::D In such situation, amplitudes are added by vector method. `A_(R) = sqrt((4)^(2) + (3)^(2) + 2(4)(3)cos phi)` `= sqrt(25 + 24cos phi)` ...(i) Now, we can substitute different values of `phi` given in different parts in the question and can find the value of `A_(R)`.

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