A block of mass $m$ is supported by two identical parallel vertical springs, each with spring stiffness constant $k$ (Fig. 11–53). What will be the frequency of vertical oscillation?

VIDEO TRANSCRIPT

This is Giancoli Answers with Mr. Dychko. We have this formula for the frequency of a simple harmonic oscillator it's 1 over 2π times the square root of the spring constant divided by m. Now, in this case the spring constant is an effective spring constant. We need to consider these 2 springs as a single spring and what would be the spring constant if we thought of this as a single spring, and that's what I'm referring to as the effective spring constant. And we can figure it out by saying that 2 times the spring force because there's two springs, each exerting a force upwards of f, spring. And the size of each of those forces is going to be spring constant times x, however much this spring has been stretched to support this mass and there are two springs and so that's why the 2 is there. And everything in front of the x is essentially the effective spring constant of the system. And so the effective spring constant is 2 k, 2 times the spring constant of a single spring. And so in this frequency formula this is always effective spring constant. And we can replace, even though, you know, you don't always write the eff there but that is, you know, we've solved problems that involve things on top of water and then all sorts of other, you know, systems that are not really springs but we have this notion of an effective spring constant, and likewise for here it's effective spring constant. And so we put in 2 k for that effective spring constant. And voila, we have 1 over 2π times square root 2 k over m is going to be the frequency