Mass-spring-damper Problems solved. Catalog 1

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: € 21.5

Below, the statements of problems solved in this guide.

1. Given the System of Figure 1, find the transfer function X_(s)/U_(s).

2. Given the System of Figure 2, find the transfer function X_(s)/Y_(s) .

3. Given the System of Figure 3, find the transfer function X_2(s)/U_(s) using its model in the frequency domain and linear algebra.

4. Given the System of Figure 4, find the transfer function Y_2(s)/U_(s):

5. Given the System of Figure 5, find the transfer function X_2(s)/U_(s). Illustrate the use of free-body diagrams.

6. Given the System of Figure 6, find the transfer functions X_1(s)/U_(s) and X_2(s)/U_(s).

7. Given the System of Figure 7, find the transfer function X_(s)/U_(s). Check the same result using the combination of state-space representation and block diagrams. Take u_(t) as the input and x_(t) as the output.

8. Given the System of Figure 8, find its state-space representation, taking x_1(t) as the output and u_(t) as the input. Build the block diagram of the system and determine the transfer function  X_1(s)/U_(s).

9.Given the System of Figure 9, find the transfer function X_2(s)/U_(s). Consider k₁= k₂=6 N/m, b₁= b₂= b₃=2 N-s/m, m₁= m₂= m₃=4 Kg. Illustrate the use of Matlab and linear algebra.

10. Given the System of Figure 10, find the transfer functions Y_1(s)/U_(s) and Y_2(s)/U_(s). Consider k₁= k₂=2 N/m, b=1 N-s/m, m₁= m₂= 2 Kg. (The same exercise is solved with state variables in the exercise 11₎

11. Find the state-space representation of the system of the previous exercise, Figure 10, taking y_2(t) as the output and u_(t) as the input. Transform the state-space representation obtained in the transfer function Y_2(s)/U_(s). Consider k₁= k₂=2 N/m, b=1 N-s/m, m₁= m₂= 2 Kg.

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You may be also interested in:

• Mass-Spring-Damper System. Problem solved. Catalog 2
• Rotational Mass-Spring-Damper System. Problem solved. Catalog 3

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