Which of the following quantities are always zero in a simple harmonic motion?
(a) Fxa
(b) vxr
(c) axr
(d) Fxr.
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|Sinθ
Direction of Force and acceleration is always same. Therefore, it will always be Zero.
(b). v × r = |v||r|Sinθ
Direction of Velocity and displacement is sometimes same,but not always thus either θ is 0 or 180, and Sine of both angles are zero.
(c). and (d). Direction of Force and acceleration is always opposite to Displacement. This means θ = 180.
∴ Sin180 = Cos90 = 0
∴ Cross product of Displacement with Force and displacement with acceleration will always be Zero.
Hence, Option (a). (b).(c). and (d) are correct. Means all are 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|Sinθ
Direction of Force and acceleration is always same. Therefore, it will always be Zero.
(b). v × r = |v||r|Sinθ
Direction of Velocity and displacement is sometimes same,but not always thus either θ is 0 or 180, and Sine of both angles are zero.
(c). and (d). Direction of Force and acceleration is always opposite to Displacement. This means θ = 180.
∴ Sin180 = Cos90 = 0
∴ Cross product of Displacement with Force and displacement with acceleration will always be Zero.
Hence, Option (a). (b).(c). and (d) are correct.