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This question already has an answer here:

Is there a rate of change force? I know that net force is rate of change of momentum or mass *acceleration.

But is there rate of change of force or (mass * jerk) ? or Rate of rate of change of force(mass *jounce) How to relate them to the physical world? Is it even physically possible?

Assuming mass to be constant

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marked as duplicate by user108787, Community Sep 16 '16 at 2:21

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Consider the force exerted by a spring on an object: $$\vec{F}=-k\vec{X},$$ where $\vec{X}$ is the deflection of the spring from its self-equilibrium. Calculate the time rate of change of the spring force:$$\frac{d\vec{F}}{dt}=-k\frac{d\vec{X}}{dt}.$$

Is the deflection changing is the spring is oscillating? Yes. So the time rate of change of the force exists. Now the real question is "Is the time rate of change of force useful for analysis in physics (as opposed to engineering/comfort/etc.)?" Generally, no. Hamiltonian mechanics answers this question in that only the first derivatives of position and momentum, along with constraints, are sufficient to describe the motions of systems.

Other responders may expand on this idea.

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In many vibration problems F = k.x = a(sin omega.t)
F prime= -omega.cos(omega.t).
So we have the rate of change of force. In structural engineering seismic design we mainly deal with a lateral force that is time dependant and we need to calculate its first and second derivatives.
All electrical motors and alternators deal with variable sinusoidal force. Internal combustion engines as well have to deal with explosion and impulses.
In applied mechanics it is hard to find a case where the force is not time dependant.

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