Springs: Simple Harmonic Motion

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SUMMARY

The discussion focuses on calculating the spring constant for a compact car with a mass of 1050 kg and its oscillation frequency when carrying additional weight. The car bounces at a frequency of 2.0 Hz, leading to the determination of the spring constant using Hooke's Law. Additionally, the frequency of oscillation with four 110 kg passengers is to be calculated, requiring an understanding of mass distribution and spring dynamics.

PREREQUISITES
  • Understanding of Hooke's Law and its application in spring mechanics
  • Knowledge of oscillation frequency calculations
  • Familiarity with mass distribution in mechanical systems
  • Basic algebra for solving equations related to physics
NEXT STEPS
  • Calculate the spring constant using the formula: k = (m * (2πf)²) where m is the mass per spring and f is the frequency.
  • Explore the effects of added mass on oscillation frequency using the formula: f = (1/2π) * √(k/m_total).
  • Review examples of harmonic motion in mechanical systems to solidify understanding.
  • Investigate real-world applications of spring dynamics in automotive engineering.
USEFUL FOR

Physics students, mechanical engineers, and automotive designers interested in understanding spring dynamics and harmonic motion in vehicles.

TJC747
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A compact car has a mass of 1050 kg. Assume that the car has one spring on each wheel, that the springs are identical, and that the mass is equally distributed over the four springs.

(a) What is the spring constant of each spring if the empty car bounces up and down 2.0 times each second?
(in N/m)

(b) What will be the car's oscillation frequency while carrying four 110 kg passengers?
(in Hz)



I know all the equations for this problem, most centrally Hooke's laws; however, I am having difficulty piecing them all together. Help would be appreciated. Thanks.
 
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List the equations you know. Which have quantities that are given in the questions?
 

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