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Question
The equation of motion of a particle is x = a cos (αt)2. The motion is ______.
Options
periodic but not oscillatory.
periodic and oscillatory.
oscillatory but not periodic.
neither periodic nor oscillatory.
Solution
The equation of motion of a particle is x = a cos (αt)2. The motion is oscillatory but not periodic.
Explanation:
As the given equation is x = a cos (αt)2 is a cosine function. Hence, it is an oscillatory motion.
Now, putting t + T in place of t
x(t + T) = a cos [α(t + T)]2 .....[∵ x(t) = a cos(αt)2]
= a cos[αt2 + αT2 + 2α t T] ≠ x (t)
Where T is supposed as a period of the function ω(t).
Hence, it is not periodic.
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