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Consider the spring-mass-damper system (SMD) mounted on a massless cart as shown in Figure 1. The mathematical model of the system is given by: d'y dy m+b+ky=b+kx dt² dt dx D Where m is the mass of the cart, x = u (input of the system), b is damping coefficient, and k is spring constant. If m=1 kg, b-2 N-s/m, and k-10 N/m. Answer the following questions: N dt Figure 1: SMD on massless cart A: Derive the transfer function of the system assuming zero initial condition. x(s) B: If the input x(t) = 2t+40 sin(t), what is X(s)? what is Y(s)? and what is y(t)?

Consider the spring-mass-damper system (SMD) mounted on a massless cart as shown in Figure 1. The mathematical model of the system is given by: d'y dy m+b+ky=b+kx dt² dt dx D Where m is the mass of the cart, x = u (input of the system), b is damping coefficient, and k is spring constant. If m=1 kg, b-2 N-s/m, and k-10 N/m. Answer the following questions: N dt Figure 1: SMD on massless cart A: Derive the transfer function of the system assuming zero initial condition. x(s) B: If the input x(t) = 2t+40 sin(t), what is X(s)? what is Y(s)? and what is y(t)?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the spring-mass-damper system (SMD) mounted on a massless cart as shown in Figure 1. The mathematical model of the system is given by: dx d'y dy +b. -+ky=b+kxx dt² dt dt Where m is the mass of the cart, x = u (input of the system), b is damping coefficient, and k is spring constant. If m=1 kg, b=2 N-s/m, and k=10 N/m. Answer the following questions: 74 Malo cart A: Derive the transfer function of the m Figure 1: SMD on massless cart system assuming zero initial condition. (Y(3) X(s). B: If the input x(t) = 2t + 40 sin(t), what is X(s)? what is Y(s)? and what is y(t)?
Transcribed Image Text:Consider the spring-mass-damper system (SMD) mounted on a massless cart as shown in Figure 1. The mathematical model of the system is given by: dx d'y dy +b. -+ky=b+kxx dt² dt dt Where m is the mass of the cart, x = u (input of the system), b is damping coefficient, and k is spring constant. If m=1 kg, b=2 N-s/m, and k=10 N/m. Answer the following questions: 74 Malo cart A: Derive the transfer function of the m Figure 1: SMD on massless cart system assuming zero initial condition. (Y(3) X(s). B: If the input x(t) = 2t + 40 sin(t), what is X(s)? what is Y(s)? and what is y(t)?
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