HELP An object undergoes simple harmonic motion in two perpendicular directions.

Question

HELP

An object undergoes simple harmonic motion in two perpendicular directions. The object's position as a function of time is given as: Express the two dimensional harmonic oscillator's distance from the origin and select it from the answers below. Be sure to simplify your expression. Next, find the expression for the object's velocity in terms of the variables used in the position equation. Be sure to add the hat decoration over any unit vectors you use. takes the object 0.750 s to complete one oscillation. What is the object's speed if its distance from the rigin (radius of the circle) is 0.250 m?

Explanation / Answer

Here

Distance From Origin = sqrt(xi^2 + yj^2)

= sqrt(L^2Cos^2(wt) + L^2Sin^2(wt))

= L*sqrt(Cos^2(wt) + Sin^2(wt))

v = dr/dt = - LSin(wt) + LCos(wt)

Magnitude = sqrt(L^2Cos^2(wt) + L^2Sin^2(wt))

= L*sqrt(Cos^2(wt) + Sin^2(wt))

= L

= 0.250 m/sec

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