Mass-spring-damper Problems solved. Catalog 2

The transfer function of a Mass-Spring-Damper System. 

In this PDF guide, the Transfer Function of the exercises that are most commonly used in the mass-spring-damper system classes that are in turn part of control systems, signals and systems, analysis of electrical networks with DC motor, is determined. electronic systems in mechatronics, etc. It is a good resource to also learn how to obtain the block diagram of the system, or the representation in state variables. Request via email – WhatsApp. Payment is provided by PayPal, Credit or debit card. Cost: € 15

Below, the statements of problems solved in this guide.

1. Given the System of Figure 12, find the transfer functions Y_1(s)/U_(s) and Y_2(s)/U_(s).

2. Given the System of Figure 13, find the transfer functions Y_1(s)/U_(s) and Y_2(s)/U_(s).

3. Given the System of Figure 14, find the transfer functions X_1(s)/U_(s)  and  X_2(s)/U_(s).

4. Given the System of Figure 15, find the transfer function X_2(s)/U_(s). Consider k₁=1, k₂= 15 N/m, b₁=4, b₂= 16 N-s/m, m₁= 8, m₂=3  Kg.

5. Given the System of Figure 16, find the transfer function X_3(s)/U_(s). Consider k₁=5, k₂= 4, k₃= 4  N/m, b₁=2, b₂= 2, b₃= 3  N-s/m, m₁= 4, m₂=5, m₃=5  Kg.

6.Given the System of Figure 17, find the transfer function X_1(s)/U_(s). Consider k₁=k₂= 1 N/m, b₁= b₂= b₃= 1  N-s/m, m₁= 2, m₂=1, m₃=1  Kg. The same exercise is solved with state variables in the next number._.

7. Find the state-space representation of the system of the previous exercise, Figure 17, taking x_1(t) as the output and u_(t) as the input. Transform the state-space representation obtained in the transfer function X_1(s)/U_(s). Consider k₁=k₂= 1 N/m, b₁= b₂= b₃= 1  N-s/m, m₁= 2, m₂=1, m₃=1  Kg.

8. Given the System of Figure 19, find the transfer function Y_h(s)/f_up(s). Consider k_h=7, k_s=8, k_ave=5  N/m, b_f=3, b_h= 10  N-s/m, m_h=1, m_f=2 Kg.

9. Given the System of Figure 20, find the transfer functions X_2(s)/U_(s) and X_3(s)/U_(s). Consider k₁=1, k₂=2, k₃=3, k₄=4 N/m, b₁=2,b₂= 1,b₃= 3 N-s/m, m₁=2,m₂=1,m₃=3  Kg.

10. Find the state-space representation of the system in Figure 21, taking x_3(t) as the output and u_(t) as the input. Transform the state-space representation obtained in the transfer function X_3(s)/U_(s). Consider k=2 N/m, b₁=b₂=b₃=b₄=b₅=1 N-s/m, m₁=2,m₂=1,m₃=1  Kg.

11. Determine the transfer function X_1(s)/ F_(s) and the block diagram of the system in Figure 22:

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You can be interested in:

• • Mass-Spring-Damper System. Problem solved. Catalog 1
  • Rotational Mass-Spring-Damper System. Problem solved. Catalog 3

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