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(Solved): Show all work step by step 4) A communication sensor on a spacecraft is modelled as a mass / spring ...
Show all work step by step
4) A communication sensor on a spacecraft is modelled as a mass spring damper as shown below. If , , and the sensor casing has length , will the sensor collide with the case wall?
Expert Answer
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 = 0where 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.