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(Solved): homework 4) A communication sensor on a spacecraft is modelled as a mass / spring/damper as shown b ...


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4) A communication sensor on a spacecraft is modelled as a mass \( / \) spring/damper as shown below. If \( \mathrm{K}=112.5
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?


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The equation of motion for the sensor is:

  
where:
m is the mass of the sensor (0.5 kg)
c is the damping coefficient (15 kg/s)
k is the spring constant (112.5 N/m)
x is the displacement of the sensor from its equilibrium position
x? is the velocity of the sensor
x¨ is the acceleration of the sensor
The initial conditions are:
  
  

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