How Do You Calculate Velocity at Equilibrium in Simple Harmonic Motion?

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Homework Help Overview

The discussion revolves around calculating the velocity of a mass-spring system at the equilibrium point during simple harmonic motion (SHM). The original poster presents a scenario involving a mass vibrating with a specified amplitude and frequency, seeking guidance on the correct approach to determine the velocity at equilibrium.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the relationship between frequency, spring constant, and velocity in SHM. Questions are raised about the correct equations to use and the implications of known variables like amplitude and frequency. Some participants suggest using energy conservation as an alternative method to find the velocity.

Discussion Status

The discussion is active, with participants sharing different approaches and equations related to the problem. There is a mix of attempts to clarify the relationships between variables and to derive the necessary equations for calculating velocity. No consensus has been reached, but several productive lines of inquiry are being explored.

Contextual Notes

Participants note the importance of understanding the relationship between frequency and the spring constant, as well as the need for clarity on the definitions and equations relevant to SHM. The original poster expresses uncertainty about the frequency, which is a critical component for solving the problem.

chazgurl4life
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A 0.55 kg mass at the end of a spring vibrates 2.0 times per second with an amplitude of 0.16 m.
(a) Determine the velocity when it passes the equilibrium point.
I have no idea how to figure this out

i mean to figure out velocity ...we use this equstion vmax= 2pi*Amplitude* Frequency

I ahve the amplitude but no frequency..im i using the right process?
 
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How is the frequency of oscillation related to the spring constant k? What else determines the frequency of oscillation? Once you have k, do you have what you need to figure out the midpoint velocity? You can also do it with energy conservation (KE + PE = constant)...
 
Ok so i know that K= (2pi*freq.)^2* mass and then once i have K i can uses vmax= 2pi Af and solve for A?
 
chazgurl4life said:
Ok so i know that K= (2pi*freq.)^2* mass and then once i have K i can uses vmax= 2pi Af and solve for A?
I thought you had the amplitude and frequency already. What is the SHM equation for the motion of the object in terms of the mass, spring constant k, amplitude and frequency?

y(t) = something * sin( something * t )

And then you can get the velocity by differentiating, right? Or else just take the easy way out and use the conservation of energy method that I mentioned.
 

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