Problem 2/18 Page 29, Engineering Mechanics - Dynamics, Meriam and Kraige, 4th Edition

Given: v(t) = v0 sin(w t) and s=s0 when t=0 for a particle moving in a straight line.

Find: s(t)

Relevant variables:

v0 = 16 mm/s
w = p/6 rad/s
s0 = 8 mm

Solution:

v = ds/dt = v0 sin(w t)

Separating variables:

ds = v0 sin(w t) dt

Integrating both sides:

s = -v0/w cos(w t) +C

Knowing that s=s0 at t=0 permits the evaluation of C:

s = -v0/w cos(w t) + v0/w + s0

As the extremes of the cosine function are 1 and -1:

smax = s0 + 2 v0/w = 69.1 mm

Plot not included at this time.