Opposing spring oscillation with mass

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SUMMARY

The discussion centers on calculating the frequency of oscillation for a 36 kg mass connected to two springs with spring constants k1 = 3 N/m and k2 = 4 N/m. The mass is placed on a horizontal frictionless surface, and the springs are positioned on opposite sides of the mass. The correct approach involves recognizing that the effective spring constant is not simply the sum of k1 and k2 due to their opposing positions. Instead, the frequency of oscillation can be determined using the formula f = (1/2π) * √(k_eff/m), where k_eff is the effective spring constant derived from the individual spring constants.

PREREQUISITES
  • Understanding of Hooke's Law and spring constants
  • Knowledge of simple harmonic motion (SHM) principles
  • Ability to calculate effective spring constants for springs in parallel
  • Familiarity with basic physics equations related to oscillation frequency
NEXT STEPS
  • Calculate the effective spring constant for springs in parallel
  • Learn the derivation of the frequency formula for oscillating systems
  • Explore examples of oscillation in mechanical systems
  • Study the impact of mass and spring constants on oscillation frequency
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Physics students, educators, and anyone interested in understanding the dynamics of oscillating systems and the principles of simple harmonic motion.

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Homework Statement


A 36 kg mass is placed on a horizontal frictionless surface and then connected to
walls by two springs with spring constants k1 = 3 N/m and k2 = 4 N/m. What is the
frequency, f (in Hz), of oscillation for the 36 kg mass if it is displaced slightly to one
side?


Homework Equations





The Attempt at a Solution


So, I wasn't sure if the spring constant added linearly or if something crazy happened. If it did then I was thinking it would be possible to plug in some numbers into the energy equations. From there plug it into the SHM equations. I'm not sure if that works at all though. Thanks!
 
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Start by drawing a free body diagram.

The springs are on opposite sides of the mass, so you can't just add them.

In equilibrium, the initial extension is zero. So if you displace it x to one side, how will the forces act?
 

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