More practice questions

4. Q4. What is the phase difference between the acceleration and the velocity in SHM, and which leads?

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   With x = A cos ωt, v = ωA cos(ωt + π/2) and a = ω^²A cos(ωt + π), so a is π/2 ahead of v.

5. Q5. At what displacement is the speed half its greatest value?

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   ω√(A^² − x^²) = ωA/2 gives A^² − x^² = A^²/4, so x = ±(√3/2)A, about ±0.87A.

6. Q6. A particle in SHM has an acceleration of −8 m/s^² when its displacement is +2 cm. Find its angular frequency and period.

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   a = −ω^²x gives ω^² = 8/0.02 = 400, so ω = 20 rad/s and T = 2π/20, about 0.314 s.