# Kinematics calculations using derivatives

The x coordinate in meters, of an object which moves on the x axis with SHM is

expressed by: x(t) = .12 Sin (5 t + .35)

a. At time t= 0, find the initial x coordinate, and the initial magnitude and direction of the velocity and the acceleration.

b. At exactly one half a period after t=0, find the x coordinate and the magnitude and direction of the velocity v and the acceleration a.

https://brainmass.com/physics/circular-motion/simple-harmonic-motion-equation-numerical-values-19691

#### Solution Preview

Physics statements:

A. A general equation giving the x coordinate of a body moving with SHM on an x axis between +Xm and -Xm, with the x axis origin at the center of motion, angular frequency w, and initial phase angle Q in radians, is:

(1) x= Xm sin( w t + Q)

B. The phase angle changes by '2 Pi' during exactly one period T, ...

#### Solution Summary

The expert examines simple harmonic motion equations given with numerical values.