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Given an equation of x(t) for a certain point moving with SHM, get v(t) and a(t), then calculate intercepts on the curves provided in ATTACHMENTS.

The position x of a certain SHM is expressed by: x = (.25 m) cos (8 t).
PART a. Take derivatives to write v(t) and a(t).
PART b. ATTACHMENT #1 shows general sine or cosine curves with the time axis shown. The location of the vertical axis, not shown, depends on the equation for t=0. For each equation, make a vertical axis and write the coordinates of its intercept, then calculate and write the time coordinates of three time intercepts to the nearest millisecond.
SEE ATTACHMENT #2 for an example.
PART c. Find the time in seconds for the point to move from +.15 m to -.10 m.


Solution Preview

PART a. In general, if y=A sin bz, then dy/dz= bA cos bz. And if y=A cos bz, then similarly, dy/dz = ...