Help with harmonic oscillation/SHM/Periodic motion question

[ztalira]

I'm a bit unsure about my answers. Help! (posting figure)
link: http://imgur.com/whExO3S

Homework Statement

http://imgur.com/whExO3S
Consider the harmonic oscillator composed of a mass and two springs of spring constants k₁ and k₂ (shown in figure). If the mass, M moves on a friction less surface, answer the following in terms of the quantities given.
a) What is the restoring force on the mass when it is displaced a distance of x to the right?
b) What is frequency of oscillation, ω, for this oscillator?

Homework Equations

ω=sqrt(k/M)
F=-kx

The Attempt at a Solution

a)[/B]
F=k₁x+k₂x=x(k₁+k₂)
b)
ω=sqrt(k/M)
since there are two force constants acting on the mass
ω=sqrt((k₁+k₂)/M)

^seems way too simple though. What am I missing?

 

[Ken G]

You are not missing anything! A good test: try setting each k to zero in turn, and make sure you get a reasonable answer.