k = 64 lb/ft for spring
position above equilirium = x
at t = 0 x = .5 ft
x = .5 cos 2 pi t/T
we need to find T, the period
f = -kx = m a
but a = .5 (2 pi/T)^2(-cos2 pi/T) =-(2pi/T)^2 x
-k x = -(2 pi/T)^2 x
2 pi/T = sqrt(k/m)
m = 128/32 = 4
2 pi/T = sqrt (64/4) = 4
x = .5 cos 4 t
at t = pi/12
x = .5 cos pi/3 = .5 cos 60deg = .25
w = 2 pi f = 2 pi/T = 4 radians/sec
f = w/2pi = 2/pi
T = pi/2
The question is really a physics question but uses old English units of feet which means to get mass (in slugs) you must divide pounds by g which is about 32 ft/s^2.
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