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thewaywewalk edited this question instead of responding to it. moving said edits to a comment instead.
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OK. as drawn, ignoring mass and accelerations, the force $F_p$ will appear as a torque on your ball screw.

However, the total force on the ball screw, and hence the torque, depends on the mass of the thing you're moving with the ball screw interacting with gravity (if it's being moved in anything other than a horizontal plane), and on whether or not the whole assembly -- frame and load -- is moving at anything other than a steady velocity.

On a bad day, your mass-spring-damper system will have an overall resonance that interacts with your control system, making oscillations happen where you never expected them.

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