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For a simple harmonic oscillator, the force is proportional to the displacement

F=-kx, where F is the force, x is the displacement, and k is a positive proportionality constant commonly referred to as the spring constant

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Q: What is the mathematical relationship between force and displacement?
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Work = Force * displacement if the displacement and the force are parallel - work is positive if force and displacement are in the same direction, negative if they have opposite direction. At an angle Work = Force * displacement * cos(θ) where θ is the angle between the force and displacement vectors.


Is the relationship between distance and force in Newton's law of universal gravitation a negative correlation?

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What is the mathematical formula for calculating work?

The mathematical formula for calculating work is: Work = Force × Distance × cos(θ) where: Work is the amount of energy transferred or expended; Force is the amount of applied force; Distance is the displacement of the object in the direction of the force; θ is the angle between the direction of the force and the direction of displacement.


What is formula of a works?

it is the dot product of displacement and force . i.e. Fdcos(A) where F is the magnitude of force , d is the magnitude of displacement and A is the angle between them


How do you find the angle in the work done?

You measure it. Depending on the information provided, you can also calculate it, for example using trigonometry. ======================== Work done= Force vector . Displacement vector=Force*displacement*cos a, where a is the angle between the force and the displacement. So you have the values of work force and displacement then you can do the cosine inverse of the ratio of work done to the product of the force and displacement. That will give you the angle.


What is the relationship of force and work?

Force is essential to perform work. When the point of application of the force gets displaced then force is said to have performed work. Work is scalar physical quantity. Where as Force and displacement are vector quantities. So the scalar product of force and displacement gives the amount of work done. Thus the work is got by the product of magnitude of force and the resolved component of the displacement in the direction of application of force.