A mass m = 13 \ kg is connected to two different springs, one on the left and another on the...

Question:

A mass {eq}m = 13 \ kg {/eq} is connected to two different springs, one on the left and another on the right. It is displaced a distance {eq}x {/eq} to the right from its equilibrium position. (Take {eq}k_1 = 115 \ N/m {/eq} and {eq}k_2 = 198 \ N/m {/eq}.)

a) What is the net force acting on the mass?

b) What is the effective spring constant?

c) What will the frequency of the oscillation be when the mass is released?

d) If {eq}x = 0.1 \ m {/eq}, what is the total energy of the mass-spring system after the mass is released, and what is the maximum velocity of the mass?

Variations in the Position of a Spring:

When there is no mass attached to the spring, the spring is at rest condition, and when a mass is attached to the spring, the spring will extend, and the end of the spring will move to a new equilibrium position. The spring responds the force applied on it such as it stretched by applying an upward direction force.

Answer and Explanation:

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Given data

  • The mass connected to two different springs is: {eq}m = 13\,{\rm{kg}} {/eq}.
  • The first spring constant is: {eq}{k_1} = 115\;{{\rm{N}}...

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Practice Applying Spring Constant Formulas

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Chapter 17 / Lesson 11
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In this lesson, you'll have the chance to practice using the spring constant formula. The lesson includes four problems of medium difficulty involving a variety of real-life applications.


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