# Equation of x(t) for a certain point moving with SHM

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.

https://brainmass.com/physics/classical-mechanics/equation-certain-point-moving-shm-6997

#### 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 = ...

#### Solution Summary

The equations of a function for certain points moving with SHM are determined. The coordinate intercepts for time equations are provided.