A small creature moves with constant speed in a vertical circle on a bright day. Does its shadow formed by the sun on a horizontal plane move in a simple harmonic motion?
Answers
yes its shadow on herizontal plane moves ina simple hermonic motion. the projection of a uniform circular motion exutes simple hermonic motion along its diamiter ( which is the shadow on the hirozintal plane), with the mean position lying at the centre of the circle
Answer ⇒ Yes. The shadow formed by the sun on a horizontal plane move in a simple harmonic motion.
Explanation ⇒ The Shadow of the Creature while moving in a circular path is always directed towards the center.
Now, when the Particle Starts moving , the displacement of the projection on the x-axis will be doing S.H.M.
Refers to the attachment for the better explanation.
From the attachment, it can be said that, If the Particle is at position y, then displacement of Projection is zero. Now, when Creature starts moving, then displacement of the Participle continue to increases on the x - axis. It becomes maximum om the Oa.
From this, It again decreases and then reaches the point opposite to y. Again, it increases upto O(-a) and then decreases upto y.
This motion is exactly similar to S.H.M. in which from the mean position, displacement first increases and then decreases and then again it increases and then decreases, and particle reaches the means position again.
Thus, we an say Particle is doing the S.H.M.
Hope it helps .
