Derivatives of Trig functions part ii.. Thm: Simple Harmonic Motion A point moving on a number line is in simple harmonic motion if its directed distance.

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Presentation transcript:

Derivatives of Trig functions part ii.

Thm: Simple Harmonic Motion A point moving on a number line is in simple harmonic motion if its directed distance d from the origin is given by either Where a and ω(omega) are real numbers and ω > 0. The motion has frequency, which is the number of oscillations per unit of time.

Ex. Suppose that an object attached to a coiled spring is pulled down a distance of 5 inches from its rest position and then released. If the time for one oscillation is 3 seconds, write an equation that relates the distance of the object from its rest position after time t.

Ex. Given a simple harmonic motion function of d = 4 sin t, What are its velocity and acceleration at time t? Describe its motion

Def: Jerk: Jerk is the derivative of acceleration. If a body’s position at time t is s(t), the body’s jerk at time t is Find the jerk in last example.