Question

Out of the following functions, representing motion of a particle, which represents SHM?
(A) y = sinωt - cosωt
(B) y = sin³ ωt
(C) y = $5\cos\bigg \lgroup \frac{3\pi}{4}-3\omega t\bigg \rgroup$
(D) y = 1+ ωt + ω²t²
(a) Only (A)
(b) Only (D) does not represent SHM
(c) Only (A) and (C)
(d) Only (A) and (B)

Answer 1

Question : Out of the following functions, representing motion of a particle, which represents SHM?

(A) y = sinωt - cosωt

(B) y = sin³ ωt

(C) y = $5\cos\bigg \lgroup \frac{3\pi}{4}-3\omega t\bigg \rgroup$

(D) y = 1+ ωt + ω²t²

solution : if equation of a particle is given by, y = f(t) it will follow simple harmonic motion only if, d²y/dt² ∝ - y

let's check all options !

(A) y = sinωt - cosωt

dy/dt = ωcosωt + ωsinωt [ after differentiating with respect to time ]

d²y/dt² = -ω²sinωt + ω²cosωt [ again differentiating w.r.t time ]

= -ω²[sinωt - cosωt] = -ω²y

i.e., d²y/dt² ∝ - y

hence option (A) follows shm.

similarly check out other options.

(B) d²y/dt² doesn't proportional to (-y)

so, option (B) doesn't follow shm.

(C) here also d²y/dt² ∝ - y

so, option (C) follow shm.

(D) it doesn't follow simple harmonic motion because it is neither trigonometric nor exponential who follows the simple harmonic motion.

Therefore option (A) and (C) represent simple harmonic motion.

Answer 2

Answer:

opt:c A and C is the answer.

Explanation:

following is the proper ques

Out of the following functions representing motion of a particle which represents S.H.M.?

    (A) y = sinωt – cosωt             (B) y = sin3ωt

    (C) y = 5cos (3π/4 -  3ωt)        (D) y = 1 + ωt + 2t2

(1) Only (A) and (B)                 (2) Only (A)

(3) Only (D) does not represent S.H.M.         (4) Only (A) and (C)

.

refer attachment for detailed answer.

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