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High School Teacher
The rest position for the spring is .5; the minimum height is .1m and the maximum height is .9m
The period is given as 1.2 seconds. The start position is at the minimum.
The general form for a sinusoid is `y=acos(b(x-h))+k` . (Here we choose cosine since the function begins at a max or min -- you can choose to use sine with a phase shift if you want.)
a gives the amplitude (and if a<0 the graph is reflected over the horizontal axis),b yields the period (`b=(2pi)/p` ), h is the horizontal translation or phase shift and k is the midline.
Here the amplitude is .4m, and a=-.4. (Began at minimum.)
h=0 there is no phase shift.
Then h(.3)=.5, h(.7)=.846,h(2.2)=.3
We assume that the spring has the same displacement in both directions and that the oscillations are not dampened (e.g. from friction, air resistance, etc...).
Posted by embizze on August 2, 2013 at 12:56 PM (Answer #1)
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