Stewart – Calculus ET 8e Chapter 17 Form G
____ 14. A spring has a mass of kg and its damping constant is . The spring starts from its
equilibrium position with a velocity of m/s. Graph the position function for the spring constant
. Select the correct answer.
a.
c.
b.
15. A spring with a 3-kg mass is held stretched 0.9 m beyond its natural length by a force of 30 N. If
the spring begins at its equilibrium position but a push gives it an initial velocity of m/s, find the
position x(t) of the mass after t seconds.
16. 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.
17. A series circuit consists of a resistor , an inductor with , a capacitor with
, and a generator producing a voltage of If the initial charge is
and the initial current is 0, find the charge at time t.
Stewart – Calculus ET 8e Chapter 17 Form G
____ 18. A spring with a mass of 2 kg has damping constant 8 and spring constant 80. Graph the position
function of the mass at time t if it starts at the equilibrium position with a velocity of 2 m/s.
Select the correct answer.
a.
c.
b.
19. Use power series to solve the differential equation..
20. The solution of the initial-value problem is called a
Bessel function of order 0. Solve the initial – value problem to find a power series expansion for
the Bessel function.
Stewart – Calculus ET 8e Chapter 17 Form G
Answer Key
Stewart – Calculus ET 8e Chapter 17 Form G
Stewart – Calculus ET 8e Chapter 17 Form H
____ 1. Solve the differential equation. Select the correct answer.
a.
b.
c.
d.
e.
2. Solve the initial-value problem.
3. Solve the boundary-value problem, if possible.
4. Solve the differential equation.
Stewart – Calculus ET 8e Chapter 17 Form H
____ 5. Solve the initial-value problem. Select the correct answer.
.
a.
b.
c.
d.
e.
6. Solve the initial-value problem.
7. Solve the boundary-value problem, if possible.
8. Solve the differential equation using the method of undetermined coefficients.
Stewart – Calculus ET 8e Chapter 17 Form H
____ 9. Solve the differential equation using the method of undetermined coefficients.
Select the correct answer.
a.
b.
c.
d.
e.
10. Solve the differential equation using the method of variation of parameters.
11. Solve the differential equation using the method of variation of parameters.
____ 12. A spring with a -kg mass has natural length m and is maintained stretched to a length of
m by a force of N. If the spring is compressed to a length of m and then released with
zero velocity, find the position of the mass at any time . Select the correct answer.
a.
b.
c.
d.
e.
Stewart – Calculus ET 8e Chapter 17 Form H
13. A spring has a mass of kg and its damping constant is . The spring starts from its
equilibrium position with a velocity of m/s. Graph the position function for the spring constant
.
14. A spring with a mass of 2 kg has damping constant 8 and spring constant 80. Graph the position
function of the mass at time t if it starts at the equilibrium position with a velocity of 2 m/s.
15. 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.
____ 16. Use power series to solve the differential equation. Select the correct answer.
a.
b.
c.
d.
e.
17. Use power series to solve the differential equation.
18. Use power series to solve the differential equation.
Stewart – Calculus ET 8e Chapter 17 Form H
____ 19. Use power series to solve the differential equation. Select the correct answer.
a.
b.
c.
d.
e.
20. The solution of the initial-value problem is called a
Bessel function of order 0. Solve the initial – value problem to find a power series expansion for
the Bessel function.
Stewart – Calculus ET 8e Chapter 17 Form H
Answer Key
Stewart – Calculus ET 8e Chapter 17 Form H