When two displacements represented by and are super- imposed the motion is

y = y1+y2 = so the resulting motion is SHM with amplitude

When two displacements represented by and are super- imposed the motion is

y = y1+y2 = so the resulting motion is SHM with amplitude

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When two displacements represented by $large {Y_1}, = ,asin left( {omega t} right)$ and $large {Y_2}, = ,bcos left( {omega t} right)$ are super- imposed the motion is

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not a simple harmonic

simple harmonic with amplitude $large frac{a}{b}$

simple harmonic with amplitude $large sqrt {{a^2} + {b^2}}$

simple harmonic with amplitude $large left( {frac{{a + b}}{2}} right)$

answer is C.

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Detailed Solution

y = y₁+y₂ = $large asin omega t + bcos omega t$

$large therefore y, = ,sqrt {{a^2} + {b^2}} sin left( {omega t + {{tan }^{ - 1}}frac{b}{a}} right)$

so the resulting motion is SHM with amplitude $large sqrt {{a^2} + {b^2}}$

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When two displacements represented by and are super- imposed the motion is

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When two displacements represented by $large {Y_1}, = ,asin left( {omega t} right)$ and $large {Y_2}, = ,bcos left( {omega t} right)$ are super- imposed the motion is