Understanding SHM: Velocity of a Mass on a Spring at Max Displacement

In summary, when a mass on a spring undergoes SHM, its instantaneous velocity is zero at the maximum displacement from equilibrium. This is because the velocity changes from positive to negative at the extrema of position.
  • #1
Dx
I am curious to know that if a mass on a spring undergoes SHM. when the mass is at its MAX displacement from equilibrium, its instantaneous velocity is what?
is it zero!

can someone explain?
Dx :wink:
 
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  • #2
Well, just before the mass hits the max displacement, the velocity is +deltaV, and just after it is -deltaV. You have to go through zero to get from + to -.
 
  • #3
Okay!

Dx scratches his head.
I said at MAX displacement that deltav is + or - Max but my teacher says I am wrong. It must be less than max but not zero as youve kinda explained, i think
Dx :wink:

Right?
 
  • #4
You had it right the first time: The speed at the extrema of position is zero.

If you are moving this way ----->
and then this way <-----

then at some point you had to stop and turn around.
 
  • #5
Kool

Hello,

Thanks!
Dx :wink:
 
Last edited by a moderator:

1. What is SHM?

SHM stands for Simple Harmonic Motion. It is a type of periodic motion where a body moves back and forth around a central equilibrium position.

2. How is the velocity of a mass on a spring at maximum displacement calculated?

The velocity of a mass on a spring at maximum displacement is equal to the product of the amplitude and the angular frequency. This can be represented by the equation v = Aω, where v is the velocity, A is the amplitude, and ω is the angular frequency.

3. What factors affect the velocity of a mass on a spring at maximum displacement?

The velocity of a mass on a spring at maximum displacement is affected by the amplitude of the oscillation, the mass of the object, and the spring constant. Additionally, the presence of any external forces or damping can also affect the velocity.

4. How does the velocity of a mass on a spring change over time?

The velocity of a mass on a spring changes over time in a sinusoidal manner. It starts at its maximum value at the equilibrium position, decreases to zero at the maximum displacement, reaches its minimum value at the opposite equilibrium position, and then returns to its maximum value at the equilibrium position again.

5. What is the relationship between the velocity and acceleration in SHM?

In SHM, the velocity and acceleration are always perpendicular to each other. The velocity is at its maximum value when the acceleration is zero, and vice versa. This relationship can also be represented by the equation a = -ω²x, where a is the acceleration, ω is the angular frequency, and x is the displacement from the equilibrium position.

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