Question

Problem 1: Trees are known as rain time machines, which is whence the ancient Canadian proverb comes: "Stand under a tree to find out what the weather was 10 minutes ago, eh." Below is an o.d.e. for a tree, where y(t) denotes the amount of rain falling out of the tree, u(t) denotes the amount of rain falling into the tree, k is some constant, and time is measured in minutes. 10? + y = ku, a) Determine a value for k¹² Explain your reasoning. b) Write the o.d.e. for time measured in seconds. c) Use MATLAB's step function to simulate the given system with time in minutes from t = 0 to t = 30 minutes. d) Use MATLAB's lsim function to simulate the unit step response for the system you made with time in seconds from t = 0 to t = 30 minutes. e) Plot both results in the same plot with time in minutes. Make one of the curves dashed to make sure we can see them both. Remember axis labels and legend.

          Problem 1: Trees are known as rain time machines, which is whence the ancient Canadian proverb
comes: "Stand under a tree to find out what the weather was 10 minutes ago, eh."
Below is an o.d.e. for a tree, where y(t) denotes the amount of rain falling out of the
tree, u(t) denotes the amount of rain falling into the tree, k is some constant, and time
is measured in minutes.
10? + y = ku,
a) Determine a value for k¹² Explain your reasoning.
b) Write the o.d.e. for time measured in seconds.
c) Use MATLAB's step function to simulate the given system with time in minutes
from t = 0 to t = 30 minutes.
d) Use MATLAB's lsim function to simulate the unit step response for the system
you made with time in seconds from t = 0 to t = 30 minutes.
e) Plot both results in the same plot with time in minutes. Make one of the curves
dashed to make sure we can see them both. Remember axis labels and legend.

Problem 1: Trees are known as rain time machines, which is whence the ancient Canadian proverb
comes: "Stand under a tree to find out what the weather was 10 minutes ago, eh."
Below is an o.d.e. for a tree, where y(t) denotes the amount of rain falling out of the
tree, u(t) denotes the amount of rain falling into the tree, k is some constant, and time
is measured in minutes.
10? + y = ku,
a) Determine a value for k¹² Explain your reasoning.
b) Write the o.d.e. for time measured in seconds.
c) Use MATLAB's step function to simulate the given system with time in minutes
from t = 0 to t = 30 minutes.
d) Use MATLAB's lsim function to simulate the unit step response for the system
you made with time in seconds from t = 0 to t = 30 minutes.
e) Plot both results in the same plot with time in minutes. Make one of the curves
dashed to make sure we can see them both. Remember axis labels and legend.

Added by Thomas D.

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