5. Give a function f(y) so that f is polynomial and y\' = f(y) has a stable equi

ID: 2962782 • Letter: 5

Question

5. Give a function f(y) so that f is polynomial and

y' = f(y) has a stable equilibrium at y=2,

and unstable equilibrium at y=5,

and a half stable equilibrium at y=9.

Begin by sketching the phase line.

6. A ball with mass 0.15kg is thrown upward with initial velocity 20m/s

from the roof of a building wich is 30m high. Ignoring air resistance,

find the maximum height above the ground that the ball reaches, and

the time at which it will hit the ground (Assuming it misses the buildingon on the way down).

7. Last night I backed a store bought frozen lasagne in a 400

6) m dv/dt + kv = mg

m = 0.15 kg
k = 1/30
g = -9.8m/s

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