Page 146 - Schaum's Outline of Differential Equations

CHAP. 14] SECOND-ORDER LINEAR DIFFERENTIAL EQUATIONS 129

14.44. A 1-slug mass is attached to a spring having a spring constant of 8 Ib/ft. The mass is initially set into motion from
the equilibrium position with no initial velocity by applying an external force F(t) = 16 cos 4t. Find the subsequent
motion of the mass, if the force due to air resistance is —4x Ib.
14.45. A 64-lb weight is attached to a spring whereupon the spring is stretched 1.28 ft and allowed to come to rest. The
weight is set into motion by applying an external force F(t) = 4 sin 2t. Find the subsequent motion of the weight if
the surrounding medium offers a negligible resistance.
14.46. A 128-lb weight is attached to a spring whereupon the spring is stretched 2 ft and allowed to come to rest. The weight is
set into motion from rest by displacing the spring 6 in above its equilibrium position and also by applying an external
force F(t) = 8 sin 4t. Find the subsequent motion of the weight if the surrounding medium offers a negligible resistance.

14.47. Solve Problem 14.38 if, in addition, the mass is subjected to an externally applied force F(t) = 16 sin 8t.
14.48. A 16-lb weight is attached to a spring whereupon the spring is stretched 1.6 ft and allowed to come to rest. The
weight is set into motion from rest by displacing the spring 9 in above its equilibrium position and also by applying
an external force F(t) = 5 cos 2t. Find the subsequent motion of the weight if the surrounding medium offers a
resistance of —2x Ib.
14.49. Write the steady-state portion of the motion found in Problem 14.48 in the form specified by Eq. (14.13).

14.50. A |--kg mass is attached to a spring having a spring constant of 6 N/m and allowed to come to rest. The mass is set
into motion by applying an external force F(t) = 24 cos 3t -33 sin 3t. Find the subsequent motion of the mass if the
surrounding medium offers a resistance of —3x N.

14.51. Write the steady-state portion of the motion found in Problem 14.50 in the form of Eq. (14.13).

14.52. An RCL circuit connected in series with R = 6 ohms, C = 0.02 farad, and L = 0.1 henry has an applied voltage
E(t) = 6 volts. Assuming no initial current and no initial charge at t = 0 when the voltage is first applied, find the
subsequent charge on the capacitor and the current in the circuit.

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14.53. An RCL circuit connected in series with a resistance of 5 ohms, a condenser of capacitance 4 X 10~ farad, and an
inductance of 0.05 henry has an applied emf E(t) = 110 volts. Assuming no initial current and no initial charge on the
capacitor, find expressions for the current flowing through the circuit and the charge on the capacitor at any time t.
14.54. An RCL circuit connected in series with R = 6 ohms, C = 0.02 farad, and L = 0.1 henry has no applied voltage. Find
the subsequent current in the circuit if the initial charge on the capacitor is -^ coulomb and the initial current is zero.
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14.55. An RCL circuit connected in series with a resistance of 1000 ohm, a condenser of capacitance 4 X 10~ farad, and
an inductance of 1 henry has an applied emf E(t) = 24 volts. Assuming no initial current and no initial charge on the
capacitor, find an expression for the current flowing through the circuit at any time t.
14.56. An RCL circuit connected in series with a resistance of 4 ohms, a capacitor of 1/26 farad, and an inductance of
1/2 henry has an applied voltage E(t) = 16 cos 2t. Assuming no initial current and no initial charge on the capacitor,
find an expression for the current flowing through the circuit at any time t.

14.57. Determine the steady-state current in the circuit described in Problem 14.56 and write it in the form of Eq. (14.13).
14.58. An RCL circuit connected in series with a resistance of 16 ohms, a capacitor of 0.02 farad, and an inductance of
2 henries has an applied voltage E(t) = 100 sin 3t. Assuming no initial current and no initial charge on the capacitor,
find an expression for the current flowing through the circuit at any time t.

14.59. Determine the steady-state current in the circuit described in Problem 14.56 and write it in the form of Eq. (14.13).
14.60. An RCL circuit connected in series with a resistance of 20 ohms, a capacitor of 10"* farad, and an inductance of
0.05 henry has an applied voltage E(t) = 100 cos 200t. Assuming no initial current and no initial charge on the
capacitor, find an expression for the current flowing through the circuit at any time t.
14.61. Determine the steady-state current in the circuit described in Problem 14.60 and write it in the form of Eq. (14.13).