Hanging a 0.5 kg mass on a lightweight spring with a spring constant of 150 N/m, the system's damping coefficient is 1.4 $\mathrm{kg/s}$. The external force applied to the system is $F \,=\, 3 \mathrm{cos} \, 6 \, t \, \mathrm{N}$. Find the steady-state values of the displacement amplitude, velocity amplitude, and acceleration amplitude; the average power loss in one cycle; the system's resonant frequency and the displacement amplitude, velocity amplitude, acceleration amplitude, and average power loss in one cycle at this frequency (with the same amplitude of applied force as before); the system's quality factor $Q_{m}$ and the bandwidth at the half-power point are( ).

Options:
A. $x_{m} \ =\ 0. 0 2 1 \ \mathrm{m}, v_{m} \ =\ 0. 1 9 \ \mathrm{m / s} \,, a_{m} \ =\ 0. 9 0 \ \mathrm{m / s}^{2} \,,\, \overline{{{{W}}}}_{R} \ =\ -\ 0. 0 1 1 \ \mathrm{W} \,, f_{r} \ =$ 2.88 Hz, $x_{\mathrm{m r}}=0. 1 2 9 \ \mathrm{m}, v_{\mathrm{m r}}=2. 1 9 \ \mathrm{m} / \mathrm{s}, a_{\mathrm{m}}=3 7. 1 5 \ \mathrm{m} / \mathrm{s}^{2} \,, \ \overline{{{{W}}}}_{\mathrm{R}}=-\, 3. 2 7 \ \mathrm{W}, \, Q_{\mathrm{m}}=2. 1 8, \Delta f$ =5.5Hz
B. $x_{m} \ =\ 0. 0 1 7 \ \mathrm{m}, v_{m} \ =\ 0. 1 1 \ \mathrm{m / s} \,, a_{m} \ =\ 0. 8 5 \ \mathrm{m / s}^{2} \,,\, \overline{{{{W}}}}_{R} \ =\ -\ 0. 0 1 7 \ \mathrm{W} \,, f_{r} \ =$ 2.79 Hz, $x_{\mathrm{m r}}=0. 1 2 5 \ \mathrm{m}, v_{\mathrm{m r}}=2. 1 2 \ \mathrm{m} / \mathrm{s}, a_{\mathrm{m}}=3 7. 2 3 \ \mathrm{m} / \mathrm{s}^{2} \,, \ \overline{{{{W}}}}_{\mathrm{R}}=-\, 3. 2 6 \ \mathrm{W}, \, Q_{\mathrm{m}}=2. 1 9, \Delta f$ =5.9Hz
C. $x_{m} \ =\ 0. 0 2 0 \ \mathrm{m}, v_{m} \ =\ 0. 1 3 \ \mathrm{m / s} \,, a_{m} \ =\ 0. 8 1 \ \mathrm{m / s}^{2} \,,\, \overline{{{{W}}}}_{R} \ =\ -\ 0. 0 1 4 \ \mathrm{W} \,, f_{r} \ =$ 2.82 Hz, $x_{\mathrm{m r}}=0. 1 2 6 \ \mathrm{m}, v_{\mathrm{m r}}=2. 1 6 \ \mathrm{m} / \mathrm{s}, a_{\mathrm{m}}=3 7. 2 0 \ \mathrm{m} / \mathrm{s}^{2} \,, \ \overline{{{{W}}}}_{\mathrm{R}}=-\, 3. 2 2 \ \mathrm{W}, \, Q_{\mathrm{m}}=2. 1 5, \Delta f$ =6.1Hz
D. $x_{m} \ =\ 0. 0 1 8 \ \mathrm{m}, v_{m} \ =\ 0. 1 2 \ \mathrm{m / s} \,, a_{m} \ =\ 0. 7 9 \ \mathrm{m / s}^{2} \,,\, \overline{{{{W}}}}_{R} \ =\ -\ 0. 0 2 1 \ \mathrm{W} \,, f_{r} \ =$ 2.68 Hz, $x_{\mathrm{m r}}=0. 1 2 0 \ \mathrm{m}, v_{\mathrm{m r}}=2. 1 0 \ \mathrm{m} / \mathrm{s}, a_{\mathrm{m}}=3 7. 0 9 \ \mathrm{m} / \mathrm{s}^{2} \,, \ \overline{{{{W}}}}_{\mathrm{R}}=-\, 3. 2 0 \ \mathrm{W}, \, Q_{\mathrm{m}}=2. 1 3, \Delta f$ =5.8Hz
E. $x_{m} \ =\ 0. 0 2 9 \ \mathrm{m}, v_{m} \ =\ 0. 1 0 \ \mathrm{m / s} \,, a_{m} \ =\ 0. 7 6 \ \mathrm{m / s}^{2} \,,\, \overline{{{{W}}}}_{R} \ =\ -\ 0. 0 1 6 \ \mathrm{W} \,, f_{r} \ =R$ 2.75 Hz, $x_{\mathrm{m r}}=0. 1 2 1 \ \mathrm{m}, v_{\mathrm{m r}}=2. 1 3 \ \mathrm{m} / \mathrm{s}, a_{\mathrm{m}}=3 7. 1 6 \ \mathrm{m} / \mathrm{s}^{2} \,, \ \overline{{{{W}}}}_{\mathrm{R}}=-\, 3. 2 5 \ \mathrm{W}, \, Q_{\mathrm{m}}=2. 1 6, \Delta f$ =6.0Hz
F. $x_{m} \ =\ 0. 0 2 3 \ \mathrm{m}, v_{m} \ =\ 0. 1 4 \ \mathrm{m / s} \,, a_{m} \ =\ 0. 8 2 \ \mathrm{m / s}^{2} \,,\, \overline{{{{W}}}}_{R} \ =\ -\ 0. 0 1 3 \ \mathrm{W} \,, f_{r} \ =$ 2.76 Hz, $x_{\mathrm{m r}}=0. 1 2 4 \ \mathrm{m}, v_{\mathrm{m r}}=2. 1 4 \ \mathrm{m} / \mathrm{s}, a_{\mathrm{m}}=3 7. 1 1 \ \mathrm{m} / \mathrm{s}^{2} \,, \ \overline{{{{W}}}}_{\mathrm{R}}=-\, 3. 2 1 \ \mathrm{W}, \, Q_{\mathrm{m}}=2. 1 4, \Delta f$ =5.9Hz
G. $x_{m} \ =\ 0. 0 2 4 \ \mathrm{m}, v_{m} \ =\ 0. 1 8 \ \mathrm{m / s} \,, a_{m} \ =\ 0. 8 7 \ \mathrm{m / s}^{2} \,,\, \overline{{{{W}}}}_{R} \ =\ -\ 0. 0 1 8 \ \mathrm{W} \,, f_{r} \ =$ 2.85 Hz, $x_{\mathrm{m r}}=0. 1 2 3 \ \mathrm{m}, v_{\mathrm{m r}}=2. 1 7 \ \mathrm{m} / \mathrm{s}, a_{\mathrm{m}}=3 7. 0 7 \ \mathrm{m} / \mathrm{s}^{2} \,, \ \overline{{{{W}}}}_{\mathrm{R}}=-\, 3. 2 8 \ \mathrm{W}, \, Q_{\mathrm{m}}=2. 1 7, \Delta f$ =5.4Hz
H. $x_{m} \ =\ 0. 0 2 8 \ \mathrm{m}, v_{m} \ =\ 0. 1 1 \ \mathrm{m / s} \,, a_{m} \ =\ 0. 7 8 \ \mathrm{m / s}^{2} \,,\, \overline{{{{W}}}}_{R} \ =\ -\ 0. 0 1 5 \ \mathrm{W} \,, f_{r} \ =$ 2.72 Hz, $x_{\mathrm{m r}}=0. 1 2 2 \ \mathrm{m}, v_{\mathrm{m r}}=2. 1 1 \ \mathrm{m} / \mathrm{s}, a_{\mathrm{m}}=3 7. 0 8 \ \mathrm{m} / \mathrm{s}^{2} \,, \ \overline{{{{W}}}}_{\mathrm{R}}=-\, 3. 2 4 \ \mathrm{W}, \, Q_{\mathrm{m}}=2. 1 5, \Delta f$ =5.7Hz
I. $x_{m} \ =\ 0. 0 2 5 \ \mathrm{m}, v_{m} \ =\ 0. 1 5 \ \mathrm{m / s} \,, a_{m} \ =\ 0. 8 3 \ \mathrm{m / s}^{2} \,,\, \overline{{{{W}}}}_{R} \ =\ -\ 0. 0 1 2 \ \mathrm{W} \,, f_{r} \ =R$ 2.90 Hz, $x_{\mathrm{m r}}=0. 1 2 8 \ \mathrm{m}, v_{\mathrm{m r}}=2. 1 8 \ \mathrm{m} / \mathrm{s}, a_{\mathrm{m}}=3 7. 1 9 \ \mathrm{m} / \mathrm{s}^{2} \,, \ \overline{{{{W}}}}_{\mathrm{R}}=-\, 3. 2 3 \ \mathrm{W}, \, Q_{\mathrm{m}}=2. 1 3, \Delta f$ =5.6Hz
J. $x_{m} \ =\ 0. 0 2 7 \ \mathrm{m}, v_{m} \ =\ 0. 1 4 \ \mathrm{m / s} \,, a_{m} \ =\ 0. 7 4 \ \mathrm{m / s}^{2} \,,\, \overline{{{{W}}}}_{R} \ =\ -\ 0. 0 1 9 \ \mathrm{W} \,, f_{r} \ =$ 2.93 Hz, $x_{\mathrm{m r}}=0. 1 2 7 \ \mathrm{m}, v_{\mathrm{m r}}=2. 1 5 \ \mathrm{m} / \mathrm{s}, a_{\mathrm{m}}=3 7. 1 4 \ \mathrm{m} / \mathrm{s}^{2} \,, \ \overline{{{{W}}}}_{\mathrm{R}}=-\, 3. 2 2 \ \mathrm{W}, \, Q_{\mathrm{m}}=2. 1 2, \Delta f$ =6.2Hz
Answer: F