Is the Velocity Zero in Equilibrium Points of a Simple Harmonic Oscillator?

In summary: That's the whole problem with stable equilibrium in SHOs.In summary, the velocity of a simple harmonic oscillator is a maximum when it passes through its equilibrium point, which is also where the potential energy is minimum. However, the extremes in position are not equilibrium points. For a pendulum with maximum points, the velocity is zero at these points due to the relationship between kinetic and potential energy. The farthest extent of position is the maximum of potential energy, and the velocity is zero there. This is the issue with stable equilibrium in SHOs.
  • #1
omri3012
62
0
Hallo,

Does the velocity i simple harmonic oscillator is zero in equilibrium points? if it's true

how does it make sense with the fact that i suppose to get a maximum kinetic

Energy in those points (stable ones)

i would really appreciate if someone could clear this issue for me.

Thanks,

Omri
 
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  • #2
The velocity of a simple harmonic oscillator is a maximum when it passes through its equilibrium point. Is that what you were asking?
 
  • #3
diazona said:
The velocity of a simple harmonic oscillator is a maximum when it passes through its equilibrium point. Is that what you were asking?

yes,

but what about the non stable equilibrium point (maximum points)?

thanks
omri
 
  • #4
Simple Harmonic Scillators have stable equilibria (or they wouldn't oscillate).

The extremes in position are not equilibrium points.
 
  • #5
JazzFusion said:
Simple Harmonic Scillators have stable equilibria (or they wouldn't oscillate).

The extremes in position are not equilibrium points.

sorry for that... i ment that if i have a potential with maximum points does the velocity
is zero there?
 
  • #6
In general, the total energy of a pendulum is T + V (kinetic plus potential energy). T + V = constant. One is a maximum when the other is minimum, and vice versa. There is one other quasistable equilibrium point for a pendulum, when the pendulum is exactly upside down. In principle, it should stay there forever, barring vibration and air currents. In actually, it is unstable, because of the Heisenberg Uncertainty Principle. If the tip of the pendulum has a momentum uncertainty Δ p, and the uncertainty in position is Δ x, then the product is Δp Δx <=h/2 pi.

Based on this uncertainty (and barring friction), the pendulum will begin swinging (as I recall) in a few seconds.

Γ Δ Θ Λ Ξ Π Σ Φ Ψ Ω
 
  • #7
omri3012 said:
sorry for that... i ment that if i have a potential with maximum points does the velocity
is zero there?
If I'm understanding your question right, YES. PE is a maximum when KE is zero, and vice versa.

The farthest extent of position is the maximum of potential energy, and V is zero.
 

FAQ: Is the Velocity Zero in Equilibrium Points of a Simple Harmonic Oscillator?

What is a simple harmonic oscillator?

A simple harmonic oscillator is a type of motion in which an object oscillates back and forth around an equilibrium position due to a restoring force that is proportional to the displacement from the equilibrium position. This type of motion can be seen in systems such as a mass attached to a spring or a pendulum swinging back and forth.

What is the equation for a simple harmonic oscillator?

The equation for a simple harmonic oscillator is F = -kx, where F is the restoring force, k is the spring constant, and x is the displacement from the equilibrium position. This equation follows Hooke's Law, which states that the force exerted by a spring is directly proportional to the amount it is stretched or compressed.

What is the period of a simple harmonic oscillator?

The period of a simple harmonic oscillator is the time it takes for one complete cycle of oscillation. It is given by the equation T = 2π√(m/k), where m is the mass of the object and k is the spring constant. This means that a larger mass or a stiffer spring will result in a longer period.

What is the amplitude of a simple harmonic oscillator?

The amplitude of a simple harmonic oscillator is the maximum displacement from the equilibrium position. It is related to the energy of the system, with a higher amplitude corresponding to a greater amount of energy. The amplitude remains constant as long as the system is undisturbed.

What is the relationship between a simple harmonic oscillator and circular motion?

There is a close relationship between a simple harmonic oscillator and circular motion. In fact, simple harmonic motion can be thought of as a projection of circular motion onto a straight line. The restoring force in a simple harmonic oscillator is analogous to the centripetal force in circular motion, and the displacement from equilibrium is analogous to the angular displacement in circular motion.

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