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Q.

The motion of a particle is given by X = A sinωt + B cosωt the motion of the particle is

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a

not simple harmonic

b

simple harmonic with amplitude A+B

c

simple harmonic with amplitude (A+B)/2

d

simple harmonic with amplitude

answer is D.

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Detailed Solution

The equation X = (A sinωt + B cosωt) A2+B2sinωt+ϕ where  ϕ=tan-1BArepresents another SHM of time period π/ω having on amplitude A2+B2.
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The motion of a particle is given by X = A sinωt + B cosωt the motion of the particle is