Simple harmonic oscillations can be modeled by the projection of circular motion at constant angular velocity onto a diameter of the circle. When this is done, the analog along the diameter of the acceleration of the particle executing simple harmonic motion is
A) the displacement from the center of the diameter of the projection of the position of the particle on the circle.
B) the projection along the diameter of the velocity of the particle on the circle.
C) the projection along the diameter of tangential acceleration of the particle on the circle.
D) the projection along the diameter of centripetal acceleration of the particle on the circle.
E) meaningful only when the particle moving in the circle also has a non-zero tangential acceleration.

Question

Quizplus · Accepted Answer

The projection of circular motion onto a diameter of the circle results in simple harmonic motion. The acceleration of the particle at any point on the circle has two components - tangential acceleration and centripetal acceleration. When the circular motion is projected onto a diameter, the tangential acceleration becomes zero as there is no component of the velocity vector along the diameter. Therefore, the analog of acceleration along the diameter of the projection of circular motion is the projection along the diameter of the centripetal acceleration, which is towards the center of the circle. This is because the centripetal acceleration is responsible for keeping the particle in circular motion and towards the center of the circle.

Simple Harmonic Oscillations Can Be Modeled by the Projection of Circular