Solving Vibrations and Waves: Mass, Spring Constant, Energy, Speed

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SUMMARY

The discussion focuses on solving problems related to mass-spring systems, specifically calculating total energy and speed. For a 5 kg mass attached to a spring with a spring constant of 13 N/cm, the total energy at maximum displacement of 20 cm is calculated to be 26 Joules. The second problem involves a 15 kg mass with a spring constant of 20 N/cm, where the speed at a displacement of 5 cm is sought, with the answer provided as 2.2 m/s. The energy stored in the spring at the moment of release is also emphasized as a key concept.

PREREQUISITES
  • Understanding of Hooke's Law and spring constants
  • Knowledge of potential energy (PE) and kinetic energy (KE) equations
  • Familiarity with energy conservation principles in mechanical systems
  • Basic algebra for solving equations involving mass, speed, and energy
NEXT STEPS
  • Learn about energy conservation in oscillatory motion
  • Study the relationship between spring constant and energy storage
  • Explore the dynamics of mass-spring systems using differential equations
  • Investigate the effects of varying mass and spring constants on system behavior
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone interested in understanding the dynamics of mass-spring systems and energy calculations in mechanical oscillations.

Elvis
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1) A 5 kg mass, m, rests on a frictionless, horizontal, wooden table top, and is attached to one end of a spring anchored at its other end . If the spring has a spring constant=13 N/cm and the mass is pulled back (in the positive direction ) 20 cm and released, to the nearest tenth of a joule, what is its total energy?
2) if the mass is 15 kg and the spring constant is 20 N/cm, to the nearest tenth of a m/s, what is its speed at x= 5 cm?

I have solved the 1st one :

1N/cm=100N/m

E = PE + KE
E = 1/2kA^2 + 1/2mv^2 At KE v=0 because the mass stops momentarily as it changes directions. Then :

E = PE
E = 1/2kA^2
E = 1/2(13*100)*(0.2)^2
E = 26J

I have problem with the second problem. please help to solve this. I have 2 hours that I am tryin to solve it . I have only the answer that is 2.2m/s.

Please help......



:cry: Lol...
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The spring is still pulled back 20 cm in part (b). Can you find how much energy is stored in it at the moment of release when v = 0?
 

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