Response of a 2-DOF spring-mass system,Equation of motion Equation of motion,Block Diagram on Simulink©, Submitted By: MEB12046 VINOD KUMAR MEB12047 ALOK P. SINGH MEB12048 ABHISHEK ANAND THAKUR MEB12049 ARJUN GOND MEB12050 KRISHNA JAISWAL

1. CONTROL SYSTEM
Response of a 2-DOF spring-mass system

2. The System
F(t)
k 2k
m m
x1
x2

3. Equation of motion


4. Equation of motion(Contd.)
 Applying LaplaceTransform on Equation 2
and taking initial conditions as zero.
𝑚𝑠2
𝑋2 𝑠 − 2𝑘𝑋1 𝑠 + 2𝑘𝑋2 𝑠 = 𝐹 𝑠
𝑚𝑠2
𝑋2 𝑠 − 2𝑘
2𝑘𝑋2 𝑠
𝑚𝑠2 + 3𝑘
+ 2𝑘𝑋2 𝑠 = 𝐹 𝑠
𝑋2 𝑠 𝑚𝑠2
−
4𝑘2
𝑚𝑠2 + 3𝑘
+ 2𝑘 = 𝐹 𝑠
𝑇. 𝐹.2 =
𝑋2 𝑠
𝐹 𝑠
=
1
𝑚𝑠2 −
4𝑘2
𝑚𝑠2 + 3𝑘
+ 2𝑘
𝑚𝑠2
+ 3𝑘

5. Equation of motion(Contd.)
𝑋1 𝑠 =
2𝑘𝑋2 𝑠
𝑚𝑠2 + 3𝑘
𝑋1 𝑠
=
2𝑘
𝑚𝑠2 + 3𝑘
×
𝑚𝑠2
+ 3𝑘
𝑚2 𝑠4 + 5𝑘𝑚𝑠2 + 2𝑘2
𝐹 𝑠
𝑇. 𝐹.1 =
𝑋1 𝑠
𝐹 𝑠
=
2𝑘
𝑚2 𝑠4 + 5𝑘𝑚𝑠2 + 2𝑘2
Taking
𝑘 = 2
𝑚 = 3

6. Block Diagram on Simulink©

7. Simulink Result

8. Thank You