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Question

A particle is executing SHM x=3cosωt+4sinωt. Find the phase shift and amplitude.
  1. 50,5 units
  2. 37,3.5 units
  3. 53,3.5 units
  4. 37,5 units

A
50,5 units
B
37,3.5 units
C
37,5 units
D
53,3.5 units
Solution
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x=3cosωt+4sinωt
lets take
x0cosϕ=4 ............(I)
and x0sinϕ=3 ............(II)
Now the equation becomes
x=x0sinϕcosωt+x0cosϕsinωtx=x0(sinϕcosωt+cosϕsinωt)x=x0sin(ωt+ϕ)
Squaring and adding (I) and (II) we get
x02(cos2ϕ+sin2ϕ)=42+32=25x0=5
dividing (II) by (I), we get
tanϕ=34ϕ=37
x=5sin(ωt+37) which represents a SHM of amplitude of 5 units and a phase of 37

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