Which one of the following equations of motion represents simple harmonic motion? where k, k0, k1 and a are all positive. (a) Acceleration = - k (x + a) (b) Acceleration = k(x + a) (c) Acceleration = -ω 2x (d) Acceleration = - k0x + k1x2

Answer: (c). SHM condition: acceleration = -ω² x (proportional to displacement and opposite to it). (b) has the wrong sign and (d) has an x² term. (a) is SHM only about a shifted mean x=-a; (c) is the standard form. (c) acceleration = -ω² x matches the definition exactly. So the answer is (c).

Which one of the following equations of motion represents simple… | NEET 2009 (AIPMT)

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Periodic Motion & SHM Basics

Which one of the following equations of motion represents simple harmonic motion? where k, k0, k1 and a are all positive.

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Answer: (c)

SHM condition: acceleration $= -\omega^2 x$ (proportional to displacement and opposite to it).
(b) has the wrong sign and (d) has an $x^2$ term.
(a) is SHM only about a shifted mean $x=-a$ ; (c) is the standard form.
(c) acceleration $= -\omega^2 x$ matches the definition exactly.
So the answer is (c).

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