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Exam 17: Second-Order Differential Equations

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Suppose a spring has mass M and spring constant k and let Suppose a spring has mass M and spring constant k and let . Suppose that the damping constant is so small that the damping force is negligible. If an external force is applied (the applied frequency equals the natural frequency), use the method of undetermined coefficients to find the equation that describes the motion of the mass. . Suppose that the damping constant is so small that the damping force is negligible. If an external force Suppose a spring has mass M and spring constant k and let . Suppose that the damping constant is so small that the damping force is negligible. If an external force is applied (the applied frequency equals the natural frequency), use the method of undetermined coefficients to find the equation that describes the motion of the mass. is applied (the applied frequency equals the natural frequency), use the method of undetermined coefficients to find the equation that describes the motion of the mass.

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Question 1
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A

Solve the initial-value problem. Solve the initial-value problem.

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Question 2
Correct Answer:
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B

Solve the differential equation. Solve the differential equation.

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(Essay)
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Question 3
Correct Answer:
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Solve the differential equation using the method of variation of parameters. Solve the differential equation using the method of variation of parameters.

(Multiple Choice)
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Question 4

The figure shows a pendulum with length L and the angle The figure shows a pendulum with length L and the angle from the vertical to the pendulum. It can be shown that , as a function of time, satisfies the nonlinear differential equation where we can use the linear approximation from the vertical to the pendulum. It can be shown that The figure shows a pendulum with length L and the angle from the vertical to the pendulum. It can be shown that , as a function of time, satisfies the nonlinear differential equation where we can use the linear approximation , as a function of time, satisfies the nonlinear differential equation The figure shows a pendulum with length L and the angle from the vertical to the pendulum. It can be shown that , as a function of time, satisfies the nonlinear differential equation where we can use the linear approximation where The figure shows a pendulum with length L and the angle from the vertical to the pendulum. It can be shown that , as a function of time, satisfies the nonlinear differential equation where we can use the linear approximation The figure shows a pendulum with length L and the angle from the vertical to the pendulum. It can be shown that , as a function of time, satisfies the nonlinear differential equation where we can use the linear approximation The figure shows a pendulum with length L and the angle from the vertical to the pendulum. It can be shown that , as a function of time, satisfies the nonlinear differential equation where we can use the linear approximation we can use the linear approximation The figure shows a pendulum with length L and the angle from the vertical to the pendulum. It can be shown that , as a function of time, satisfies the nonlinear differential equation where we can use the linear approximation The figure shows a pendulum with length L and the angle from the vertical to the pendulum. It can be shown that , as a function of time, satisfies the nonlinear differential equation where we can use the linear approximation The figure shows a pendulum with length L and the angle from the vertical to the pendulum. It can be shown that , as a function of time, satisfies the nonlinear differential equation where we can use the linear approximation The figure shows a pendulum with length L and the angle from the vertical to the pendulum. It can be shown that , as a function of time, satisfies the nonlinear differential equation where we can use the linear approximation The figure shows a pendulum with length L and the angle from the vertical to the pendulum. It can be shown that , as a function of time, satisfies the nonlinear differential equation where we can use the linear approximation The figure shows a pendulum with length L and the angle from the vertical to the pendulum. It can be shown that , as a function of time, satisfies the nonlinear differential equation where we can use the linear approximation

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Question 5

Use power series to solve the differential equation. Use power series to solve the differential equation.

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Question 6

Solve the differential equation using the method of variation of parameters. Solve the differential equation using the method of variation of parameters.

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Question 7

Find a trial solution for the method of undetermined coefficients. Do not determine the coefficients. Find a trial solution for the method of undetermined coefficients. Do not determine the coefficients.

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Question 8

A spring with a mass of A spring with a mass of kg has damping constant 28 and spring constant . Find the damping constant that would produce critical damping. kg has damping constant 28 and spring constant A spring with a mass of kg has damping constant 28 and spring constant . Find the damping constant that would produce critical damping. . Find the damping constant that would produce critical damping.

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Question 9

Solve the differential equation using the method of undetermined coefficients. Solve the differential equation using the method of undetermined coefficients.

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Question 10

Solve the differential equation. Solve the differential equation.

(Multiple Choice)
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Question 11

Use power series to solve the differential equation. Use power series to solve the differential equation.

(Multiple Choice)
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Question 12

Solve the differential equation. Solve the differential equation.

(Multiple Choice)
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Question 13

Solve the differential equation using the method of undetermined coefficients. Solve the differential equation using the method of undetermined coefficients.

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Question 14

Solve the differential equation using the method of variation of parameters. Solve the differential equation using the method of variation of parameters.

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Question 15

Solve the initial-value problem. Solve the initial-value problem. . .

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Question 16

A series circuit consists of a resistor A series circuit consists of a resistor , an inductor with , a capacitor with , and a -V battery. If the initial charge is 0.0008 C and the initial current is 0, find the current I(t) at time t. , an inductor with A series circuit consists of a resistor , an inductor with , a capacitor with , and a -V battery. If the initial charge is 0.0008 C and the initial current is 0, find the current I(t) at time t. , a capacitor with A series circuit consists of a resistor , an inductor with , a capacitor with , and a -V battery. If the initial charge is 0.0008 C and the initial current is 0, find the current I(t) at time t. , and a A series circuit consists of a resistor , an inductor with , a capacitor with , and a -V battery. If the initial charge is 0.0008 C and the initial current is 0, find the current I(t) at time t. -V battery. If the initial charge is 0.0008 C and the initial current is 0, find the current I(t) at time t.

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Question 17

Solve the differential equation. Solve the differential equation.

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Question 18

Solve the differential equation using the method of undetermined coefficients. Solve the differential equation using the method of undetermined coefficients.

(Essay)
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Question 19

Solve the differential equation using the method of variation of parameters. Solve the differential equation using the method of variation of parameters.

(Essay)
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Question 20
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