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If f(1)(t)=A sin omega t and f(2)(t)=B c...

If `f_(1)(t)=A sin omega t and f_(2)(t)=B cos omegat` represent two functions, then express, then express the combined amplitude.

Text Solution

Verified by Experts

`f(t)=f_(1)(t)+f_(2)(t)=C sin (omegat+phi)`
where `C=sqrt(A^(2)+B^(2)), phi = tan^(-1)((B)/(A))`
Here .C. is the combined amplitude and `.phi.` the resultant phase.
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Knowledge Check

  • The function sin^(2)(omegat) represents :

    A
    a periodic, but not simple harmonic motion with a period `2pi//omega`
    B
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    C
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    D
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    B
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    D
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    A
    Satement-I is true, statement -II is false.
    B
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