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Which of the Following Relationships Between the Acceleration A And the Displacement X Of a Particle Involve Simple Harmonic Motion? - Physics

Which of the following relationships between the acceleration a and the displacement x of a particle involve simple harmonic motion?

(a) a = 0.7x

(b) a = –200x2

(c) a = –10x

(d) a = 100x3

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Solution 1

A motion represents simple harmonic motion if it is governed by the force law:

F = –kx

ma = –k

`:. a = k/m  x`


F is the force

m is the mass (a constant for a body)

x is the displacement

a is the acceleration

k is a constant

Among the given equations, only equation a = –10 is written in the above form with `k/m = 10`

Hence, this relation represents SHM.

Solution 2

Only (c) i.e., a = – 10x represents SHM. This is because acceleration is proportional and opposite to displacement (x).

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NCERT Class 11 Physics Textbook
Chapter 14 Oscillations
Q 6 | Page 358
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