How Do You Calculate Maximum Speed in Spring Oscillations?

AI Thread Summary
To calculate the maximum speed of a mass attached to a spring undergoing simple harmonic oscillations, the spring constant is determined to be 88.0 N/m, and the oscillation frequency is 1.00 Hz. The amplitude of the oscillation is given as the initial displacement of 0.200 m. The maximum speed can be derived using the conservation of energy principle, specifically by calculating the initial potential energy with the formula Ep = 1/2 kX^2. This approach eliminates the need to consider time or angular velocity in the calculation. The discussion concludes with a confirmation of the solution method.
K3nt70
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[SOLVED] More Spring oscillation

Homework Statement


A 2.20 kg mass is attached to a spring and placed on a horizontal, smooth surface. A horizontal force of 17.6 N is required to hold the mass at rest when it is pulled 0.200 m from its equilibrium position (the origin of the x axis). The mass is now released from rest with an initial displacement of xi = 0.200 m, and it subsequently undergoes simple harmonic oscillations. Calculate the maximum speed of the mass.

I've calculated the following already:
Spring constant is 88.0 N/m
Oscillation frequency is 1.00 Hz



Homework Equations


This is pretty much the problem; i don't know what equation to use to get the max velocity



The Attempt at a Solution


Ive been messing around with V = -AwSin(wt) but i can't fathom how to get amplitude..
 
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HINT: The amplitude is given in the question.
 
mkay, well the only thing i can see close to amplitude is Xi. But if that's amplitude, then all i have left to find is time..
 
K3nt70 said:
mkay, well the only thing i can see close to amplitude is Xi. But if that's amplitude, then all i have left to find is time..
xi is indeed the amplitude. However, there is no need to consider the amplitude, period, angular velocity etc. This problem can be trivially solved using conservation of energy.
 
Ek = 1/2 mv^2, but i don't have kenetic energy...
 
K3nt70 said:
Ek = 1/2 mv^2, but i don't have kenetic energy...
No you don't have the kinetic energy, but you can work out the initial potential energy...
 
Ep= 1/2 kX^2 <-- is this the equation you're referring to?
 
K3nt70 said:
Ep= 1/2 kX^2 <-- is this the equation you're referring to?
Indeed it is, and since energy is conserved you can use this to determine the velocity of the mass at any point.
 
woohoo! Thanks for your help!
 
  • #10
K3nt70 said:
woohoo! Thanks for your help!
No problem :smile:

Don't forget to mark the thread as 'solved' when your done.
 
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