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# A particle is executing SHM x=3cosωt+4sinωt. Find the phase shift and amplitude.50∘,5 units37∘,3.5 units53∘,3.5 units37∘,5 units

A
53,3.5 units
B
37,5 units
C
50,5 units
D
37,3.5 units
Solution
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#### x=3cosωt+4sinωtlets take x0cosϕ=4 ............(I)and x0sinϕ=3 ............(II)Now the equation becomesx=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=5dividing (II) by (I), we gettanϕ=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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