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4) A communication sensor on a spacecraft is modelled as a mass $/$ spring $/$ damper as shown below. If $K=112.5N/m$, $C=15kg/s,M=0.5kg,x(0)=0,v(0)=1.5m/s$, and the sensor casing has length $L=0.01m$, will the sensor collide with the case wall?

To determine whether the sensor will collide with the case wall

we need to solve for the motion of the mass using the given parameters and initial conditions. The equation of motion for the system is:

mx'' + cx' + k*x = 0

where m is the mass, c is the damping coefficient, k is the spring constant, x is the displacement from the equilibrium position, and x' and x'' are the first and second derivatives of x with respect to time, respectively.