The motion of the particle is given by the equation x = Asin ω t + Bcos ω t. The motion of the particle is (a) simple harmonic with amplitude (A + B) (b) simple harmonic with amplitude (A - B) (c) simple harmonic with amplitude (A² + B²)1/2 (d) not simple harmonic

Answer: (c). Write A = Rcos φ, B = Rsin φ: x = Rsin (ω t + φ). This is a single sine term, so the motion is SHM. R = √(A² + B²) = (A² + B²)1/2. So the answer is (c).

The motion of the particle is given by the equation x = Asin ω t +… | MHT CET 2025 (23 Apr, Shift 2)

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Periodic Motion & SHM Basics

The motion of the particle is given by the equation $x = A\sin\omega t + B\cos\omega t$ .

The motion of the particle is

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Answer: (c)

Write $A = R\cos\phi$ , $B = R\sin\phi$ : $x = R\sin(\omega t + \phi)$ .
This is a single sine term, so the motion is SHM.
$R = \sqrt{A^2 + B^2} = (A^2 + B^2)^{1/2}$ .
So the answer is (c).

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