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Is classical mechanics applicable as to what extent F=dp/dt would make sense as p=0 but we are applying an external force,when a force is applied on one end of a massless spring while the other end is grounded, will there be an oscillation about new position(F/k) if the equations of motion are still valid. Can the physical behavior be plotted?

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  • $\begingroup$ have a look at answers here physics.stackexchange.com/q/143140 $\endgroup$
    – anna v
    Jun 4, 2016 at 6:29
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    $\begingroup$ Why would "classical mechanics" not be valid? I'm not sure what you're asking. $\endgroup$
    – ACuriousMind
    Jun 6, 2016 at 10:11
  • $\begingroup$ @ACuriousMind I hope the edit makes it clearer. $\endgroup$ Jun 7, 2016 at 4:55

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Start with a conventional mass on a massless spring and see what happens if we let the mass go to zero. The equation of motion for the mass $m$ on a spring with force constant $k$ is:

$$ x = A\sin\left(\sqrt{\frac{k}{m}}t\right) + B\cos\left(\sqrt{\frac{k}{m}}t\right) $$

where we get the constants $A$ and $B$ from the velocity and position at time $t=0$.

The problem is that as $m\rightarrow 0$ the fraction $k/m$ becomes undefined so the equation no longer makes sense. The best we can do is take very tiny but still non-zero values of $m$, in which case the frequency is inversely proportional to $1/\sqrt{m}$.

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  • $\begingroup$ Hmm. I took the massless object to be the spring not the mass attached. $\endgroup$
    – garyp
    Jun 4, 2016 at 11:40
  • $\begingroup$ @garyp: correct, and my approach is to start with a spring + mass then remove the mass by letting $m\rightarrow 0$ to leave just the massless spring. It is in the process of doing this that you see the equation of motion becomes undefined. $\endgroup$ Jun 4, 2016 at 11:56
  • $\begingroup$ Oh. So you think the question is about a massless spring with no mass attached. That wasn't clear to me. If the OP is not happy with your answer, he or she should edit the question to clarify it. $\endgroup$
    – garyp
    Jun 4, 2016 at 13:30
  • $\begingroup$ So what i can infer from this is, it oscillates about x=F/k but the vibration cannot be studied since the equation doesn't describe the behavior around F/k as the function sin(1/√x) does not settle down on any value, the limit as x approaches 0 from the right does not exist. $\endgroup$ Jun 7, 2016 at 5:06
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Is classical mechanics valid when a force is applied on one end of a massless spring(assuming we can have a massless spring, or can't we? "yes we can") while the other end is grounded"

yes is valid

"will there be an oscillation about new position(F/k) if the equations of motion are still valid."

correct

Can the physical behavior be plotted? yes , sure

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