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Question
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`
Where,
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 x 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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