Question

Which of the following quantities are always positive in a simple harmonic motion?
(a) F.a
(b) v.r
(c) a.r
(d) F.r.

Answer 1

For the motion to be simple Harmonic, Force must be linearly proportional to the displacement.

Alos, F = -kx

a = -ω²x

v = ± ω√(A² - x²)

(a). F.a = |F||a|Cosθ

Direction of Force and acceleration is always same. Therefore, it will always be positive.

(b). v.r = |v||r|cosθ

Direction of Velocity and displacement is sometimes same,but not always thus it is npt 100% correct.

(c). and (d).  Direction of Force and acceleration is always opposite to Displacement.

∴ Dot product of Displacement with Force and displacement with acceleration will always be negative.

Hence, Option (a) is correct.

Hope it helps.

Answer 2

For the motion to be simple Harmonic, Force must be linearly proportional to the displacement.

Alos, F = -kx

a = -ω²x

v = ± ω√(A² - x²)

(a). F.a = |F||a|Cosθ

Direction of Force and acceleration is always same. Therefore, it will always be positive.