Consider a spring-mass damper system whose block of mass “m” is connected to the top wall by a spring. The input is the applied force “u(t)” and the output is the displacement “y(t)” measured from the equilibrium position. It is expected that the applied force “u(t)” must overcome the friction and the spring force while the remainder is used to accelerate the mass. i..Draw a well-labelled diagram depicting the given information about the spring-mass damper system. ii.Derive a second order differential equation for the system. iii..Derive the state-space models for the system. iv.Identify the matrices A, B, C and D from your models derived in (c).
Consider a spring-mass damper system whose block of mass “m” is connected to the top wall by a spring. The input is the applied force “u(t)” and the output is the displacement “y(t)” measured from the equilibrium position. It is expected that the applied force “u(t)” must overcome the friction and the spring force while the remainder is used to accelerate the mass.
i..Draw a well-labelled diagram depicting the given information about the spring-mass damper system.
ii.Derive a second order differential equation for the system.
iii..Derive the state-space models for the system.
iv.Identify the matrices A, B, C and D from your models derived in (c).
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