Physics Help Forum Determine the natural frequency

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 Feb 23rd 2017, 05:15 PM #1 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
 Feb 24th 2017, 12:36 PM #2 Physics Team     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.

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