Question

For the SDOF system of Fig. 1, given m=10 kg, k = 4000 N/m, and c =200 Ns/m, calculate: (a) The undamped natural frequency. (b) The damped natural frequency. (c) The resonance frequency. (d) The peak frequency (where the amplitude of the response is maximum). (e) The steady-state amplitude of the response at resonance. (f) The peak steady-state amplitude (at the peak frequency). (g) Verify your results in (e) and (f) using numerical integration for the equation of motion using MATLAB (ode45). Fig. 1 x(t) k c F(t) = sin(?t)

          For the SDOF system of Fig. 1, given m=10 kg, k = 4000 N/m, and c =200 Ns/m, calculate:
(a) The undamped natural frequency.
(b) The damped natural frequency.
(c) The resonance frequency.
(d) The peak frequency (where the amplitude of the response is maximum).
(e) The steady-state amplitude of the response at resonance.
(f) The peak steady-state amplitude (at the peak frequency).
(g) Verify your results in (e) and (f) using numerical integration for the equation of motion using MATLAB (ode45).

Fig. 1
x(t)
k
c
F(t) = sin(?t)

Show more…

For the SDOF system of Fig. 1, given m=10 kg, k = 4000 N/m, and c =200 Ns/m, calculate:
(a) The undamped natural frequency.
(b) The damped natural frequency.
(c) The resonance frequency.
(d) The peak frequency (where the amplitude of the response is maximum).
(e) The steady-state amplitude of the response at resonance.
(f) The peak steady-state amplitude (at the peak frequency).
(g) Verify your results in (e) and (f) using numerical integration for the equation of motion using MATLAB (ode45).

Fig. 1
x(t)
k
c
F(t) = sin(?t)

Added by Matthew M.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Adriano Chikande

Step 1

The external force is \(F(t) = \sin(t)\), but this will mainly come into play for the numerical integration part. ### (a) The undamped natural frequency (\(\omega_n\)) ** Show more…

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For the SDOF system of Fig. 1, given m = 10 kg, k = 4000 N/m, and c = 200 Ns/m, calculate: (a) The undamped natural frequency. (b) The damped natural frequency. (c) The resonance frequency. (d) The peak frequency (where the amplitude of the response is maximum). (e) The steady-state amplitude of the response at resonance. (f) The peak steady-state amplitude (at the peak frequency). (g) Verify your results in (e) and (f) using numerical integration for the equation of motion using MATLAB (ode45).

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