Solving SHM Spring Mass Homework Problem

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SUMMARY

The discussion focuses on solving a spring-mass oscillation problem involving a spring with an unstretched length of 60.5 cm and a maximum deformation spring force of 88.7 N. The period of oscillation was calculated to be 1.58 seconds using the formula T = 2π(m/k)^(0.5). To find the mass (m), participants are advised to use the relationship kx = mg, where k is the spring constant and x is the displacement from the equilibrium position. The discussion emphasizes the importance of determining the spring constant (K) first to facilitate the calculation of mass and energy in the oscillation.

PREREQUISITES
  • Understanding of Hooke's Law (kx = mg)
  • Familiarity with the formula for the period of oscillation (T = 2π(m/k)^(0.5))
  • Knowledge of energy in oscillations (E = 1/2kA²)
  • Basic algebra for solving equations and substitutions
NEXT STEPS
  • Calculate the spring constant (K) using the provided spring force and displacement values.
  • Determine the mass (m) by rearranging the equation kx = mg after finding K.
  • Explore the relationship between amplitude and energy in oscillations (E = 1/2kA²).
  • Investigate the effects of varying spring constants on oscillation periods.
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and oscillatory motion, as well as educators looking for examples of spring-mass systems in action.

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Homework Statement



A spring of unstretched length L0 = 60.5 cm and spring constant K is suspended vertically as shown. A mass m is attached to the spring and it stretches the spring to a length of 123 cm. Then the mass is pulled down an additional 8.74 cm from the equilibrium position and released. At its maximum deformation, the spring force is 88.7 N.

A. What is the period of the oscillation?
B. What is the mass m?
C. What is the spring constant K?
D. What is the energy in the oscillation?

Homework Equations



kx=mg T=2pi(m/k)^.5 E= 1/2kA2


The Attempt at a Solution



I found the period as 1.58s by doing (stretched - unstretched) / 9.8 and then sq root that then multiply by 2pi. However, I am completely lost on how to find mass. Using substitution, etc always gets me a negative number. Once I know how to get mass it'll be easy to find K and Energy. Thanks
 
Physics news on Phys.org
You want to find k first. Use the info you were given in the last sentence.
 

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