A steel ball weighing 128 pounds is suspended from a spring. This stretches the spring 128/401 feet.
The ball is started in motion from the equilibrium position with a downward velocity of 5 feet per second.
The air resistance (in pounds) of the moving ball numerically equals 4 times its velocity (in feet per second) .
Suppose that after t seconds the ball is y feet below its rest position. Find y in terms of t. (Note that this means that the postiive direction for y is down.)
y=?????
Take as the gravitational acceleration 32 feet per second per second.
The ball is started in motion from the equilibrium position with a downward velocity of 5 feet per second.
The air resistance (in pounds) of the moving ball numerically equals 4 times its velocity (in feet per second) .
Suppose that after t seconds the ball is y feet below its rest position. Find y in terms of t. (Note that this means that the postiive direction for y is down.)
y=?????
Take as the gravitational acceleration 32 feet per second per second.
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Mass is weight/(gravitational acceleration), so
m = 128/32 = 4 slugs.
The spring constant, assuming Hooke's Law, is determined by the given displacement
F = 128lb = k(128/401) ft ==> k = 401 lb/ft.
The damping constant is given as 4 (slug/sec). The IVP you have to solve, with the "down is positive" orientation is
4y'' + 4y' + 401y = 0, y(0) = 0, y'(0) = 5
Solving this should be straight forward.
m = 128/32 = 4 slugs.
The spring constant, assuming Hooke's Law, is determined by the given displacement
F = 128lb = k(128/401) ft ==> k = 401 lb/ft.
The damping constant is given as 4 (slug/sec). The IVP you have to solve, with the "down is positive" orientation is
4y'' + 4y' + 401y = 0, y(0) = 0, y'(0) = 5
Solving this should be straight forward.