How Do You Calculate the Frequency and Maximum Velocity of a Mass on a Spring?

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SUMMARY

The discussion focuses on calculating the frequency and maximum velocity of a mass attached to a spring, specifically using the equations of motion for springs. The mass causes a vertical spring to extend 25mm to its equilibrium position, and after being displaced an additional 20mm, the displacement at 0.05 seconds is measured at 19.2mm. Key formulas include the angular frequency w = sqrt(k/m) and the period T = 2π√(k/m), where k is the spring constant and m is the mass. The calculations demonstrate that the period can be determined without knowing the spring constant by substituting known variables.

PREREQUISITES
  • Understanding of Hooke's Law and spring constants
  • Basic knowledge of angular frequency and oscillatory motion
  • Familiarity with gravitational force calculations
  • Ability to manipulate algebraic equations for physics problems
NEXT STEPS
  • Learn how to derive the spring constant (k) using experimental data
  • Study the relationship between mass, spring constant, and frequency in oscillatory systems
  • Explore the concept of damping in spring-mass systems
  • Investigate the effects of varying mass on the frequency of oscillation
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Students studying physics, engineers working with mechanical systems, and anyone interested in understanding the dynamics of spring-mass systems.

Kev1n
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1. A mass attached to the lower end of a vertical spring causes the spring to extend 25mm to its equilibrium position. The mass is then displaced a further 20mm and released. A trace of the vibration and time measurements are taken. From these measurements it can be seen that the displacement from equilibrium position is 19.2 when the time is 0.05s
A. Calculate the expected frequeny of vibration, B. Calculate the maximm velocity of the mass. I have struggled here as ther is no (k) for the spring or mass
It would be appreciated if anyone could havea look over at my attempt and comment, thanks




2. w=sqrt(k/m), mg=kl, m=kl/g



3. A. w=sqrt (k/m), l = 25mm so 0.25m, g =9.81
m = l/g = 0.025
Basically now can see where to go without k
 
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To find the period of a spring you do not need to know the mass or the spring constant.

Substitute the calculation for the spring constant into the equation for the period, you should find that you are left with only variables you are able to calculate.

T = 2[tex]\pi[/tex][tex]\sqrt{\frac{k}{m}}[/tex]

k = [tex]\frac{F}{x}[/tex]

And think about the calculation for F.
 

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