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?
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Last edited by ChipB; Feb 24th 2017 at 01:14 PM.
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