Simple harmonic motion (doubt in the derivation of equation)

In summary, when discussing a mass attached to a horizontal spring, the equation F=-kx can be rearranged to a= -ω2x. By defining ω2=k/m, we can see that the solution to the differential equation will be a sinusoidal function with an angular frequency of ω = √(k/m). This is obtained by solving the differential equation, which can be found in the link provided.
  • #1
kandyfloss
7
0
F=-kx when talking about a mass at the end of a horizontal spring
therefore ma=-kx
rearranging we get a= -(k/m)x
then it says if we define ω2=k/m we then have a generic form :
a= -ω2x
My question is what does "if we define ω2=k/m" mean? where does this come from?is it just any random assumption?
 
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  • #2
kandyfloss said:
My question is what does "if we define ω2=k/m" mean? where does this come from?is it just any random assumption?
They define it that way because they already know the answer. The solution to the differential equation ma=-kx (or m d2x/dt2 = -kx) will be a sinusoidal function with an angular frequency given by ω = √(k/m).
 
  • #3
I didn't get it.How do you find the angular frequency from the sinusoidal function of ma=-kx (or m d2x/dt2 = -kx ?
 
  • #5
aah! great stuff,thanx.
 

What is simple harmonic motion?

Simple harmonic motion is a type of periodic motion in which a system oscillates back and forth around a central equilibrium point, with a restoring force that is directly proportional to the displacement from the equilibrium point. This type of motion is commonly seen in systems such as springs, pendulums, and mass-spring systems.

What is the equation for simple harmonic motion?

The equation for simple harmonic motion is x = A cos(ωt + φ), where x is the displacement from the equilibrium point, A is the amplitude of the oscillation, ω is the angular frequency, and φ is the phase constant. This equation is derived from the principles of Newton's second law and Hooke's law.

How is the equation for simple harmonic motion derived?

The equation for simple harmonic motion can be derived using the principles of Newton's second law and Hooke's law. By applying these laws to a mass-spring system, we can obtain the differential equation mx'' + kx = 0, where m is the mass and k is the spring constant. Solving this equation leads to the equation x = A cos(ωt + φ).

What is the significance of the angular frequency in simple harmonic motion?

The angular frequency, ω, in simple harmonic motion determines the speed at which the system oscillates and the period of the motion. A larger value of ω corresponds to a faster oscillation and a shorter period, while a smaller value of ω results in a slower oscillation and a longer period.

Can the equation for simple harmonic motion be used for all types of oscillating systems?

No, the equation for simple harmonic motion is only applicable to systems where the restoring force is directly proportional to the displacement from the equilibrium point. Other types of oscillating systems, such as damped oscillators or forced oscillators, require different equations to describe their motion.

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