Simple harmonic oscillations can be modelled by the projection of circular motion at constant angular velocity onto a diameter of the circle. When this is done, the analogue along the diameter of the acceleration of the particle executing simple harmonic motion is:
A)the displacement from the centre 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

When a circular motion is projected onto a diameter, the component of the velocity along the diameter becomes the velocity of the simple harmonic motion. The acceleration of the simple harmonic motion is then given by the projection of the centripetal acceleration on the circle along the diameter. Therefore, the analogue along the diameter of the acceleration of the particle executing simple harmonic motion is the projection along the diameter of the centripetal acceleration of the particle on the circle, which is option D.

Simple Harmonic Oscillations Can Be Modelled by the Projection of Circular