The displacement of a particle performing S.H.M. is given by Y = Acos [π(t + φ)]. If at t = 0, the displacement is y = 2 cm and velocity is 2π cm/s, the value of amplitude A in cm is (a) 2 (b) √(2) (c) 2√(2) (d) 1/√(2)

Answer: (c). Let θ = πφ. At t = 0: Acos θ = 2. v = -π Asin θ = 2π ⇒ Asin θ = -2 A = √(2² + 2²) = 2√(2) cm So the answer is (c) 2√(2).

The displacement of a particle performing S.H.M. is given by Y = Acos… | MHT CET 2024 (2 May, Shift 2)

Q29MHT CET 2024 · 2 MAY · SHIFT 2Medium

Periodic Motion & SHM Basics

The displacement of a particle performing S.H.M. is given by $Y = A\cos[\pi(t + \phi)]$ . If at $t = 0$ , the displacement is $y = 2\text{ cm}$ and velocity is $2\pi\text{ cm/s}$ , the value of amplitude $A$ in cm is

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Answer: (c)

Let $\theta = \pi\phi$ . At $t = 0$ : $A\cos\theta = 2$ .
$v = -\pi A\sin\theta = 2\pi \Rightarrow A\sin\theta = -2$
$A = \sqrt{2^2 + 2^2} = 2\sqrt{2}\text{ cm}$
So the answer is (c) $2\sqrt{2}$ .

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