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Q2
(NDA-I/2013)
Science & Technology › Basic Science (Physics, Chemistry, Biology) › Basic mechanics concepts
Answer Verified
The displacement of a particle is given by x = cos^ 2.wt. The motion is
Result
Your answer:
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·
Correct:
A
Explanation
The correct answer is Option 1. The displacement function is given by x = cos²(ωt). Using the trigonometric identity, we can rewrite this as x = [1 + cos(2ωt)] / 2, or x = 1/2 + 1/2 cos(2ωt).
A motion is Simple Harmonic Motion (SHM) if the displacement can be expressed in the form x = A cos(Ωt + φ) relative to a mean position. In this case, the particle oscillates about a mean position of x = 1/2 with an amplitude of 1/2 and an angular frequency of 2ω.
- Why Option 1 is correct: The expression is a single cosine function of time, which satisfies the differential equation for SHM (d²x/dt² ∝ -x).
- Why Option 2 is incorrect: Since it perfectly fits the SHM criteria after transformation, it is not merely periodic but specifically simple harmonic.
- Why Option 3 is incorrect: The function repeats its values at regular intervals (T = π/ω), confirming it is periodic.
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