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Write an equation that relates the distance d of the object from its rest position after t seconds.

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An object of mass m (in grams) attached to a coiled spring with damping factor b (in grams per second) is pulled down
a distance a (in centimeters) from its rest position and then released. Assume that the positive direction of the motion is up and the period is T (in seconds) under simple harmonic motion.

(a) Write an equation that relates the distance d of the object from its rest position after t seconds.
(b) Graph the equation found in part (a) for 5 oscillations using a graphing utility.

m = 25,    a = 10,     b = 0.7,       T = 5
asked Jan 29, 2015 in PRECALCULUS by anonymous

1 Answer

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Step 1:

(a)

The displacement of the object at image is image.

The damping factor image.

Mass of the object is image.

The time period image.

Time Period image.

image

The displacement by an oscillating object from rest position at time secs is

image

Substitute the values image, image, image and image in the above equation.

image

image

Step 2:

(b)

Graph the function image.

Graph the function for 5 oscillations.

image

Solution:

(a) The displacement by an oscillating object is image.

(b) Graph of the displacement of the object for 5 oscillations is

image

answered Feb 2, 2015 by Lucy Mentor

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