Simple harmonic motion and natural vibrations

Abstract

This chapter presents the concept of simple harmonic motion and natural vibrations. Simple harmonic motion is defined as a periodic motion of a point along a straight line, such that its acceleration is always toward a fixed point in that line and is proportional to its distance from that point. Simple harmonic motion may be considered as the projection on a diameter of a movement at uniform speed around the circumference of a circle. The expressions for velocity and acceleration can be derived from that for displacement by differentiating with respect to time. The negative signs in the expressions for velocity and acceleration show that for the position of X in a diagram both velocity and acceleration are in the opposite direction from the displacement. Displacement and acceleration are always in opposite directions. The unit for oscillation per second is called the hertz. Motion closely approximating to simple harmonic motion occurs in a number of natural or free vibrations.