The expression "k÷m" being equal to "w^2" (where "k" represents the spring constant and "m" represents the mass) is specific to the context of simple harmonic motion or oscillation. Let's break it down:
In simple harmonic motion, a mass attached to a spring undergoes back-and-forth oscillation around an equilibrium position. The key defining characteristic of simple harmonic motion is that the restoring force acting on the mass is directly proportional to its displacement from the equilibrium position and always directed towards the equilibrium position.
According to Hooke's Law, the restoring force (F) exerted by a spring is given by the equation F = -kx, where "k" is the spring constant and "x" is the displacement from the equilibrium position. The negative sign indicates that the force is always opposite to the direction of displacement.
Now, let's consider the equation of motion for simple harmonic motion. Applying Newton's second law, which states that force equals mass times acceleration (F = ma), we can equate the restoring force (-kx) to the mass (m) times acceleration (a). This gives us the equation -kx = ma.
Rearranging the equation, we have ma + kx = 0, which can be rewritten as a + (k/m)x = 0.
Comparing this equation to the general form of the equation of motion for simple harmonic motion, a + ω^2x = 0, we see that the angular frequency (ω) is related to the spring constant (k) and mass (m) through the equation ω^2 = k/m.
Hence, in the context of simple harmonic motion or oscillation, the expression "k÷m" is equal to "w^2" because it represents the relationship between the spring constant, mass, and angular frequency that govern the oscillatory behavior of the system.