Suppose that after t seconds the ball is y cm below its rest

Suppose that after t seconds the ball is y cm below its rest position. Find y in terms of t. (Note that this means that the postiive direction for y is down.)

A steel ball with mass 19 grams is suspended from a spring. The spring constant for this spring is 3 cm/sec^2. The ball is started in motion from the equilibrium position with a downward velocity of 3 cm per second. The air resistance of the moving ball numerically equals 0.8 times its velocity (in cm per second) . Suppose that after t seconds the ball is y cm below its rest position. Find y in terms of t. (Note that this means that the postiive direction for y is down.) y=

Solution

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A steel ball with mass 15 grams is suspended from a spring. The spring constant for this spring is 3 cmsec2.

The ball is started in motion from the equilibrium position with a downward velocity of 5 cm per second.
The air resistance of the moving ball numerically equals 0.2 times its velocity (in cm per second) .

Suppose that after t seconds the ball is y cm below its rest position. Find y in terms of t. (Note that this means that the postiive direction for y is down.)

y=??

Answer

k=0.03 m*s^2

v=0.05 m/s

m*d^2y/dt^2=-ky-a(dy/dt)+F(t)

15y\'\' + 0.2y\' + 3y = 0, y(0) = 0, y\'(0) = 5

So y(t)=11.1816e^(-0.0066667t)sin(0.447164t)