Note: Only the steady state sinusoid response amplitude |x| = A |G(io))| is of interest in...

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Note: Only the steady state sinusoid response amplitude |x| = A |G(io))| is of interest in Problems 1, 2 and 3, and not the full response. Problem 1: Consider a container of mass M = 10 kg that contains a specimen of mass m = 2 kg as shown in Fig. 1. The friction between the specimen and the bottom of the container is modelled as viscous friction with viscous friction coefficient b = 20 N s/m. The container can slide horizontally on the floor F with no friction. A horizontal force f(t) pushes the container, as shown. a) Write the equations of motion of the system. b) Find the transfer function G(s) from the input force f(t) to the horizontal displacement x(t) of the specimen. c) Consider a sinusoid input force f(t) = 5 sin 4t N. Find the steady-state amplitude |x| of the displacement sinusoid response x(t) of the specimen. f(t) m x(t) Fig. 1: Container with specimen M F Note: Only the steady state sinusoid response amplitude |x| = A |G(io))| is of interest in Problems 1, 2 and 3, and not the full response. Problem 1: Consider a container of mass M = 10 kg that contains a specimen of mass m = 2 kg as shown in Fig. 1. The friction between the specimen and the bottom of the container is modelled as viscous friction with viscous friction coefficient b = 20 N s/m. The container can slide horizontally on the floor F with no friction. A horizontal force f(t) pushes the container, as shown. a) Write the equations of motion of the system. b) Find the transfer function G(s) from the input force f(t) to the horizontal displacement x(t) of the specimen. c) Consider a sinusoid input force f(t) = 5 sin 4t N. Find the steady-state amplitude |x| of the displacement sinusoid response x(t) of the specimen. f(t) m x(t) Fig. 1: Container with specimen M F