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You put a 56.7 gram mass on a spring, set it in motion with a small amplitude, and count 10...

Question:

You put a 56.7 gram mass on a spring, set it in motion with a small amplitude, and count 10 cycles. Those 10 cycles took 3.43 seconds. What is kSHM?

Spring Constant:

In simple word, a constant which represent the total amount of force required to stretch a spring by one-unit length is generally represented by the term spring constant. Usually, the Newton per meter (N/m) unit is used to represent the spring constant of a spring.

Answer and Explanation: 1


Given- The mass is {eq}m=56.7\ \text{g}=56.7\times {{10}^{-3}}\ \text{kg} {/eq}, the number of cycles is {eq}n=10 {/eq}, the time taken is {eq}t=3.43\ \text{s} {/eq}.


By using the following relation, the time period is calculated as,

{eq}T=\dfrac{t}{n}\Rightarrow T=\dfrac{3.43\ \text{s}}{10}\Rightarrow T=0.343\ \text{s} {/eq}


By using the following relation, the spring constant is calculated as,

{eq}k=m{{\left( \dfrac{2\pi }{T} \right)}^{2}}\Rightarrow k=\left( 56.7\times {{10}^{-3}}\ \text{kg} \right){{\left( \dfrac{2\pi }{0.343\ \text{s}} \right)}^{2}}\Rightarrow k=19.02\ \text{N/m} {/eq}


Thus, the spring constant is 19.02 N/m.


Learn more about this topic:

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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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