Question

Consider a double Spring-Mass-Damper System as shown in the figure below: U >F(t) A. Create a Simulink model to simulate the dynamics of the above system for the following parameter values: F(t) = Step input force of magnitude 5 N ml = 7 kg, b1 = 3 Nsec/m, kl = 4 N/m m2 = 3 kg, b2 = 1 Nsec/m, k2= 2 N/m B. Submit a snapshot of the Simulink model created, and the Scope output for a simulation time of 50 seconds. Make sure that the Scope block plots the displacements of both masses (x1(t) and x2(t)) on the same axis. C. Comment on the nature of the displacement plots obtained in part (b). Which of the two masses (ml or m2) has greater displacement values? Is this consistent with the values of the masses (ml and m2) mentioned in part (a)?

Solve the question in Matlab and please show Matlab code

Answer 1

Solution

Free Body Diagram

x, Fit) M. م ( kg ( X2 - X جرم ,kx ہے (ii) , حل , نا

Using Newton's law,

k2(12 - 11) + b2 12-11) - k121 – 6111 = m01

-k (12 - 11) – 62.12 - 11)+F(t) = mzër

ï1 = — (k2(12 – 11) + b2(2 - 01) - k101 - 6101) mi

22 = (-k2(22 - .01) - 62.02 - .01) + F(t)) m2

SIMULINK Model

Using the equations above we can construct the following SIMULINK model

+ + 1/7 int 1 int2 1/m1 Add Add2 k 1 x1 and x2 Add3 - 1/3 0 int3 int4 1/ m2 Step Add 1

Scope Output

5 . ......... 35EE. . 21. ..... O 5 10 15 20 25 30 35 40 45 50

From the plot we can observe that $m_2$ has higher displacement compared to $m_1$ .