Insights Blog
-- Browse All Articles --
Physics Articles
Physics Tutorials
Physics Guides
Physics FAQ
Math Articles
Math Tutorials
Math Guides
Math FAQ
Education Articles
Education Guides
Bio/Chem Articles
Technology Guides
Computer Science Tutorials
Forums
Intro Physics Homework Help
Advanced Physics Homework Help
Precalculus Homework Help
Calculus Homework Help
Bio/Chem Homework Help
Engineering Homework Help
Trending
Featured Threads
Log in
Register
What's new
Search
Search
Search titles only
By:
Intro Physics Homework Help
Advanced Physics Homework Help
Precalculus Homework Help
Calculus Homework Help
Bio/Chem Homework Help
Engineering Homework Help
Menu
Log in
Register
Navigation
More options
Contact us
Close Menu
JavaScript is disabled. For a better experience, please enable JavaScript in your browser before proceeding.
You are using an out of date browser. It may not display this or other websites correctly.
You should upgrade or use an
alternative browser
.
Forums
Homework Help
Introductory Physics Homework Help
Particle with mass m and force F(t). Show that x = x(t)
Reply to thread
Message
[QUOTE="kafn8, post: 5854011"] [h2]Homework Statement [/h2] A particle of mass m is initially at rest at x = 0. It is acted upon by a force [itex]F = A cosh (\beta t)[/itex] [COLOR=#4d4dff] (1)[/COLOR] A) Show that at very small values of t, the position is approximately given by [itex]x(t) = \frac{1}{2}\frac{F_0}{m}t^2[/itex] [COLOR=#4d4dff](2)[/COLOR], where [itex]F_0[/itex] is the force at [itex]t =0[/itex] [h2]Homework Equations[/h2][h2]The Attempt at a Solution[/h2] If [itex]F(t) = Acosh(\beta t) = ma(t)[/itex] then [itex]a(t) = \frac{A}{m}cosh(\beta t)[/itex] Integrating twice yields the position such that [itex]x(t) = \frac{A}{\beta^2 m}\left[ cosh(\beta t) - 1 \right][/itex], [COLOR=#4d4dff](3)[/COLOR] Also, [itex]F_0(t=0)=m\left[\frac{A}{m}cosh(\beta(0)) \right]=A[/itex] With that out of the way, I've tried taking the limit of [COLOR=#4d4dff](3)[/COLOR] as [itex]t \rightarrow 0[/itex] but end up with the following: $$\lim_{t \rightarrow 0}x(t) = \lim_{t \rightarrow 0} \frac{A}{\beta^2 m}\left[ cosh(\beta (0)) - 1 \right]$$ $$= \frac{A}{\beta^2 m}\left[ (1) - 1 \right]$$ $$= 0$$ But all this says is that for very small values of time, the particle barely moves away from x=0. This does not directly confirm that [COLOR=#4d4dff](2)[/COLOR] is a good approximation. Any guidance is much needed and greatly appreciated! [/QUOTE]
Insert quotes…
Post reply
Forums
Homework Help
Introductory Physics Homework Help
Particle with mass m and force F(t). Show that x = x(t)
Back
Top