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Chapter 5: Q3E (page 271)
In Problems 3鈥�6, find the critical point set for the given system.
The critical points are
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In Problem 36, if a small furnace that generates 1000 Btu/hr is placed in zone B, determine the coldest it would eventually get in zone B has a heat capacity of per thousand Btu.
In Problems 3 鈥� 18, use the elimination method to find a general solution for the given linear system, where differentiation is with respect to t.
Use the result of Problem 31 to prove that all solutions to the equation\({\bf{y'' + }}{{\bf{y}}^{\bf{3}}}{\bf{ = 0}}\)remain bounded. [Hint: Argue that \(\frac{{{{\bf{y}}^{\bf{4}}}}}{{\bf{4}}}\) is bounded above by the constant appearing in Problem 31.]
A double pendulum swinging in a vertical plane under the influence of gravity (see Figure5.35) satisfies the system
When andare small angles. Solve the system when
.
In Problems 3鈥�6, find the critical point set for the given system.
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