x=−Acosωt
−A+a=−A cosωτ ...(i)
−A+3a=−A cos(ω2τ) ...(ii)
∴−1+Aa=−cosωτ ...(iii)
and −1+A3a=−cos(2ωτ) ...(iv)
Adding (iii) and (iv)
2=3cos(ωτ)−2 cos2(ωτ)+1
∴2 cos2(ωτ)−3 cos(ωτ)+1=0
∴cosωτ=21
∴ωτ=3π
∴T=6τ
A particle moves with simple harmonic motion in a straight line. In first τ s, after starting from rest it travels a distance a, and in next τ s it…
JEE Main 2014 — Physics Waves & Oscillations
2014mcqhard
A particle moves with simple harmonic motion in a straight line. In first τs, after starting from rest it travels a distance a, and in next τs it travels 2a, in same direction, then :
Official previous-year question
Held on 6 Apr 2014 · Verified 6 Jul 2026.
Options
- A
Amplitude of motion is 3a
- B
Time period of oscillations is 8τ
- C
Amplitude of motion is 4a
- D
Time period of oscillations is 6τ
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