The correct option is D 37∘,5 units
x=3cosωt+4sinωt
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∘