q_a_14

See also Class Notes 110309

110302 Differential Equations

Question:

`q001.  Solve the equation m y '' + k y = 0.

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Question:

`q002.  Solve the equation m y '' + k y = sin(omega_1 * t).  The method of undetermined coefficients, with an appropriate trial function, will suffice to find the required particular solution.

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Question:

`q003.  Solve the equation m y '' + delta * y ' + k y = 0.

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Question:

`q004.  Solve the equation m y '' + delta * y ' + k y = sin(omega_1 t).  The method of undetermined coefficients, with an appropriate trial function, will suffice to find the required particular solution.

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Question:

`q005.  Consider the function y = e^( (delta + sqrt( delta^2 - 4 k m) / 2 m * t).

If delta = 0, what is the simplified expression for the function?

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If delta = 2 sqrt( k m ), what is the simplified expression for the function?

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If delta = 4 sqrt( k m)_, what is the simplified expression for the function?

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Question:

`q006.  Consider the function

y = A e^( (delta + sqrt( delta^2 - 4 k m) / 2 m * t) + B e^( (delta + sqrt( delta^2 - 4 k m) / 2 m * t).

Write this function with e^(delta / (2 m) * t ) factored out.

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Simplify this expression for the case when delta = 0.

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Simplify this expression for the case when delta = 2 sqrt( k m ).

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Simplify this expression for the case when delta = 4 sqrt( k m ).

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Sketch a graph of each function, and describe each.

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