In Fig 06 a schematic diagram of a suspension system is shown, where the wheel a

Question

In Fig 06 a schematic diagram of a suspension system is shown, where the wheel and mounting bracket can be assumed to be of negligible mass. The input x is from trio road whilst the output y a the response of the mats m. Snow that the system's equation of motion is given by: Where the dot notation has its usual meaning m=mass c=damping coefficient k=spring rate Using Laplace transforms and assuming zero initial conditions (see Q 7 ) show that the system transfer function is given by If X(s) is a step input to model hitting a kerb stone briefly describe how you would create this system's simulation in MATLAB Simulink. Briefly explain the attraction of using simulation methods to investigate dynamic systems.

Explanation / Answer

1) Writing equation of motion for mass 'm' Total Force = Mass* acceleration m d^2y/dt^2 + ky + c dy/dt = kx + c dx/dt 2) From 1) taking Laplace transform on both sides m*s^2* y(s) - s*y(0) - y' (0) + k*y(s) + c*s*y(s) - y(0) = k*x(s) + c*s*x(s) - x(0) It is given that initial condition is zero therefore y(0) , y' (0) & x(0) would be zero therefore y(s)/x(s) = c*s + k/( m*s^2 + c*s + k) iii) solution of (ii) can be converted to a time domain by taking inverse Laplace transform which can be analyzed easily in MATLAB iv) Dynamic systems are time dependent and can be simulate easily in frequency and time domain

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