# For a given equation x(t) of SHM with initial phase non-zero, obtain v(t) and a(t) then make graphs of all three functions. Must show intercepts.

The position x of a certain SHM is expressed by: x = (.36 m) cos (6 t + .628).

PART a. Take derivatives to write v(t) and a(t).

PART b. ATTACHMENT #1 shows general sine or cosine curves with anly a time axis. The location of the vertical axis, not shown, depends on the equation. For your x(t) and v(t) and a(t), locate the 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 of similar work.

PART c. Construct a reference circle and show one radius xm at t=0 and another somewhere in the first quadrant after through angle 6t.

https://brainmass.com/physics/work/7005

#### Solution Preview

PART a.

<br>To take derivatives, recall that if, for example, z= A sin (bt + n), then the derivative dz/dt= b A cos (bt + n).

<br>For x(t) as ...