A 0.66 kg mass is attached to a light spring with a force constant of 23.9 N/m and set into...

Question:

A 0.66 kg mass is attached to a light spring with a force constant of 23.9 N/m and set into oscillation on a horizontal friction-less surface. If the spring is stretched 5.0 cm and released from rest, determine the following.

(a) maximum speed of the oscillating mass m/s

(b) speed of the oscillating mass when the spring is compressed 1.5 cm m/s

(c) speed of the oscillating mass as it passes the point 1.5 cm from the equilibrium position m/s

(d) value of x at which the speed of the oscillating mass is equal to one-half the maximum value

Simple Harmonic Motion:

Simple harmonic motion is an oscillatory motion in which the net acceleration acting on the body performing simple harmonic motion is directed towards the equilibrium position.

If a force acts on a spring of spring constant "k" and compresses it by a distance "x", then the potential energy stored in the spring is given by {eq}E_P= \dfrac{1}{2}kx^2 {/eq}.

Also, the restoring force generated by the spring is given as {eq}F=kx {/eq}

Answer and Explanation:

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Given:

Mass attached to the light spring is m = 0.66 kg.

Spring constant is k = 23.9 N/m.

The extension of the spring is x = 5.0 cm = 0.05 m.

PART...

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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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