A C B equilibrium

The amplitude of vibration is the distance from the equilibrium position to its point of greatest displacement. The period of a vibrating object is the time required to complete one vibration.

Simple harmonic motion: the acceleration a of the object is directly proportional to the negative of its displacement d from its rest position. That is, a = -kd, k > 0.

Theorem Simple Harmonic Motion An object that moves on a coordinate axis so that its distance d from the origin at time t is given by either

The frequency f of an object in simple harmonic motion is the number of oscillations per unit of time. Thus,

Frequency goes up. Period (1) goes up (2) goes down (3) stays the same

Suppose that the distance d (in centimeters) an object travels in time t (in seconds) satisfies the equation (a) Describe the motion of the object. Simple harmonic (b) What is the maximum displacement from its resting position?

Suppose that the distance d (in centimeters) an object travels in time t (in seconds) satisfies the equation (c) What is the time required for one oscillation? (d) What is the frequency?

Theorem Damped Motion The displacement d of an oscillating object from its at rest position at time t is given by where b is a damping factor (damping coefficient) and m is the mass of the oscillating object.

What damping factor makes for no decay? (1) -1 (2) 0 (3) 1