With what frequency does the spring oscillate?

Question

Suppose that a weight on a spring has initial position s(0) and period P. If s(0) = -5 in. and P = 2.5 sec, find a
function s given by s(t) = a cos ωtthat models the displacement of the weight.  With what frequency does the
spring oscillate?

Answer 1

s(t) = a cos(ωt)

 

s(0) = -5 = a cos(0) = a ⇒

 

s(t) = -5 cos(ωt),

 

s(t) in inches

 

ω = 2π/P = 2π/2.5 rad/s = ? rad/s

 

s(t) = -5 cos[(2π/2.5)t],

 

with t in seconds and s(t) in inches.