The force acting on a particle moving along X-axis is F = -k(x-v₀t) where k is a positive constant. An observer moving at a constant velocity v₀ along the X-axis looks at the particle. What kind of motion does he find for the particle?
Answers
Answer ⇒ Motion is an Simple Harmonic Motion also written as S.H.M.
Explanation ⇒ Any Oscillatory Motion in which the force is acting in opposite direction of the displacement. And Force is directly proportional to negative of displacement, then the motion will be simple Harmonic.
If this condition is proved in the given case, then the motion will be the simple harmonic motion.
Let us see, what is condition in given question.
An Observer is moving with an constant velocity v₀, and he is watching an particle which is moving in a x-axis, having F = -k(x-v₀t)
∴ F = -kx + v₀tk
The v₀tk is the force which was observed by the Observers due to his non-inertial frame. But there is no force like that in the particle. (It is pseudo Force).
∴ Actual Force acting on a particle moving in x-axis is given by,
F = -kx
therefore, F α -x
Thus, force is proportional to negative of displacement.
Hence, the motion of the Particle is Simple Harmonic Motion.
Hope it helps.