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.
Answers
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.
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.