Posted by anisah on Sunday, April 22, 2012 at 3:45am.
a steel ball weighing 128 lb is suspended from a spring, whereupon the spring is stretched 2 ft from its natural length. the ball is started in motion with no initial velocity by displacing it 6 in above the equilibrium position. assuming no damping force, find an expression for
a)the position of the ball at any time.
b)the position of the bal at t=pai/12 sec
c)the circular frequency, natural frequency and period for this system

math  Damon, Sunday, April 22, 2012 at 5:30am
k = 64 lb/ft for spring
position above equilirium = x
at t = 0 x = .5 ft
so
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
so
k x = (2 pi/T)^2 x
2 pi/T = sqrt(k/m)
m = 128/32 = 4
so
2 pi/T = sqrt (64/4) = 4
therefore
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

actually ancient physics  Damon, Sunday, April 22, 2012 at 5:32am
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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