Solve the following model of spring mass system for the given damping coefficients: u"+bu '+u = sin(mt), u (0) = 2, u '(0)=0 (iii) b=3 (i) b=0.5 (ii) b=2 Discuss the damping and graph of the solution in each case.

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Free Damped Vibrations

Free vibration is a type of vibration in which the external force is removed after giving the initial displacement to a body/system. In other words, in this type of vibration, force is applied at the initial displacement of the system, and after the initial displacement, force is removed, and the system vibrates at the natural frequency.