# Force on a massless spring [closed]

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?

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

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 $1/\sqrt{m}$.

• Hmm. I took the massless object to be the spring not the mass attached. Jun 4, 2016 at 11:40
• @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. Jun 4, 2016 at 11:56
• 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. Jun 4, 2016 at 13:30
• 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. Jun 7, 2016 at 5:06

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