Inertia balance/restoring force

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The discussion centers on the differences in restoring forces when an inertial balance is oriented horizontally versus vertically. In the horizontal position, the restoring force remains constant due to the consistent gravitational force acting on the mass. Conversely, when the balance is vertical, the restoring force varies because the components of gravitational force and spring force interact differently. This complexity can be better understood through visual aids, such as diagrams of the experimental setup. Clarifying these concepts is essential for grasping the mechanics of inertial balances in different orientations.
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A while ago I did a lab experiment using an inertial balance (oscillating horizontally) to calculate the inertial and gravitational mass of an unkown object. Following, the inertial balance was clamped under the edge of the bench with the balance extending downward. My teacher said that the restoring force is different when the balance is oriented horizontally and vertically; he said that when oriented vertically the restoring force is not constant while the horizontal restoring force is constant. can anyone please explan and elaborate!


I realize that it has something to do with the components of the force of gravity being in the same plane as the components of the spring force and the restoring force, but i get confused when i draw it out
 
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It's best if you include an illustration of the experimental setup so it'll be a lot clearer. Otherwise it's kind of hard to visualise it.
 

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