1. Solve problem by means of the method based on the discrete-time transition matrix.

2. Solve problem for the triangular pulse shown in Fig 4.32 with T = 0.1 s. Caution: Do not confuse the pule duration T with the sampling period T.

3. Solve problem by means of the convolution sum. Plot the response using the sampling period T = 0.003 s and the number sampling times n = 200.

Derive the response of a viscously damped single-degree-of-freedom system to the force F(t) = F ₀ e ^-?t ?(t) by means of the convolution integral. Plot the response for the system parameters m = 12 kg, c = 24 N ? s/m, k = 4,800 N/m and the force parameter F ₀ = 200 N, ? = 1.

Figure 4.32

These problem from Leonard Meirovitch book for fundamental of mechanical vibration.

Fo F(t) T 2 T