What Is the Angular Frequency of Oscillation for a Mass Between Two Springs?

[woaini]

Homework Statement

A mass of 9.96*10^-27kg is centered in between two springs which have a spring constant of 73N/m and 27N/m respectively. The other side the spring is pushing on is solid and does not move. What is the angular frequency of oscillation of the mass?

k1=75
k2=27
m=9.96*10^-27

Homework Equations

ω=\sqrt{k/m}

The Attempt at a Solution

I am unsure what to do with this equation. Do I add the two constants together to solve for the frequency?

This is my answer if I do so:
ω=1.00200602*10^14 Hz

 

[haruspex]

Do I add the two constants together to solve for the frequency?

Do the usual: write out the forces when the mass is displaced x from the equilibrium position, and obtain the ODE.
Note that you are not told whether the springs are relaxed in that position.

 

[rock.freak667]

If you consider the system like this,

|--k₁--m---k₂--|

If you move the mass m to the right, then the mass will compress the spring 2 by some distance x and lengthen spring 1 by a distance x.

In which direction would the spring forces be acting (remember a spring force is a restorative force so it will try to restore the spring to its initial position) ?

If you find the resultant of these two forces, it will be the same as ma where 'a' is the resultant acceleration.

You can then solve for 'a' to get something in the form of a = -ω²x where ω is your angular frequency