Which of the following dot products is always positive (never negative) during simple harmonic motion? (A) F. a (B) v. F (C) a. r (D) F. r

F. a
v. F
a. r
F. r

Correct answer: F. a

Solution

In SHM, F = -kx and a = -(omega²)x are always in the same direction (anti-parallel to displacement). So F.a = |F||a| cos(0) > 0 (zero only at equilibrium), while v can be in any direction relative to F, and F and r are always anti-parallel giving F.r < 0.

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