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Question

- 50∘,5 units
- 37∘,3.5 units
- 53∘,3.5 units
- 37∘,5 units

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Solution

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lets take

x0cosϕ=4 ............(I)

and x0sinϕ=3 ............(II)

Now the equation becomes

x=x0sinϕcosωt+x0cosϕsinωt⇒x=x0(sinϕcosωt+cosϕsinωt)⇒x=x0sin(ωt+ϕ)

Squaring and adding (I) and (II) we get

⇒x02(cos2ϕ+sin2ϕ)=42+32=25⇒x0=5

dividing (II) by (I), we get

tanϕ=34⇒ϕ=37∘

⇒x=5sin(ωt+37∘) which represents a SHM of amplitude of 5 units and a phase of 37∘

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