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The displacement of a particle varies with time according to t

Question

The displacement of a particle varies with time according to the relation $y = a s inω t + b cos ω t .$

The motion is oscillatory but not SHM.

The motion is SHM with amplitude a + b.

The motion is SHM with amplitude

a^{2} + b^{2}

The motion is SHM with amplitude

a^{2} + b^{2}

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The displacement of a particle varies with time according to the relation

y = a s inω t + b cos ω t .

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Text solutionVerified

Given

x = a s inω t + b cos ω t

.......(i)

Let

a = A cos ϕ

........(ii)

and

b A s in ϕ

..........(iii)

Squaring adding (ii) and (iii), we get

a^{2} + b^{2} = A^{2} co s^{2} ϕ + A^{2} s i n^{2} ϕ = A^{2}

Eq.(i) can be written as

x = A cos ϕ s inω t + A s in ϕ cos ω t = A s in (ω t + ϕ)

It is equation of SHM with amplitude

A = a^{2} + b^{2}

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Question Text	The displacement of a particle varies with time according to the relation $y = a s inω t + b cos ω t .$
Answer Type	Text solution:1
Upvotes	152