Go Back   Physics Help Forum > College/University Physics Help > General Physics

General Physics General Physics Help Forum

Like Tree2Likes
  • 2 Post By ChipB
Reply
 
LinkBack Thread Tools Display Modes
Old Feb 23rd 2017, 05:15 PM   #1
cxz
Junior Member
 
Join Date: Feb 2017
Posts: 5
Determine the natural frequency

Determine the natural frequency in Hz of the system sketched below given the following values:
Mass m=10kg
Spring stiffness k=18kN/m
Length a=114mm
Length b=120mm

I know that ω=(k/m)^0.5
So probably I need to calculate m.
Should I write m=10*9.81*(0.114+0.12)?
Attached Thumbnails
Determine the natural frequency-capture.jpg  
cxz is offline   Reply With Quote
Old Feb 24th 2017, 12:36 PM   #2
Physics Team
 
ChipB's Avatar
 
Join Date: Jun 2010
Location: Naperville, IL USA
Posts: 2,271
I assume you know that the natural frequency for a simple spring mass system comes from the solution to the differential equation:

$\displaystyle m\ddot x + k x = 0$

The solution of which gives the natural frequency $\displaystyle \omega = \sqrt {k/m}$, right?

The trick in this problem is that the lever arm serves to "magnify" the spring force acting on m by a factor of (a/b). If we set up variables x and y where x = left-right displacement of the mass and y = up-down displacement of the spring, you have:

x = (b/a) y

Spring force = ky,

Force acting on m = (a/b) times the spring force, or (a/b) ky.

The differential equation for motion of mass m is:

$\displaystyle m \ddot x + (a/b) k y = 0$

Sub y = (a/b) x to get:

$\displaystyle m \ddot x + (a/b)^2 kx = 0$

Can you take it from here?
topsquark and cxz like this.

Last edited by ChipB; Feb 24th 2017 at 01:14 PM.
ChipB is offline   Reply With Quote
Reply

  Physics Help Forum > College/University Physics Help > General Physics

Tags
determine, frequency, natural



Thread Tools
Display Modes


Similar Physics Forum Discussions
Thread Thread Starter Forum Replies Last Post
determine extension bigh Energy and Work 1 Sep 27th 2014 05:50 PM
Resonance,Resonance frequency,natural frequency? hyungjko Waves and Sound 1 Feb 7th 2013 01:33 PM
Water natural convection Rockandroll Thermodynamics and Fluid Mechanics 1 Dec 3rd 2012 01:44 PM
Strain and natural length werehk Equilibrium and Elasticity 3 Jul 27th 2009 10:10 PM
Determine H? reverseswing Advanced Electricity and Magnetism 1 Jun 19th 2009 03:52 AM


Facebook Twitter Google+ RSS Feed