Ellen Says That Whenever the Acceleration Is Directly Proportional to the Displacement

question 36

Multiple Choice

Ellen says that whenever the acceleration is directly proportional to the displacement of an object from its equilibrium position, the motion of the object is simple harmonic motion. Mary says this is true only if the acceleration is opposite in direction to the displacement. Which one, if either, is correct?

• A)Ellen, because \( \omega \)2 is directly proportional to the constant multiplying the displacement and to the mass.
• B)Ellen, because \( \omega \)2 is directly proportional to the mass.
• C)Mary, because \( \omega \)2 is directly proportional to the constant multiplying the displacement and to the mass.
• D)Mary, because \( \omega \)2 is directly proportional to the mass.
• E)Mary, because the second derivative of an oscillatory function like sin( \( \omega \)t) or cos( \( \omega \)t) is always proportional to the negative of the original function.

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Definitions:

Sharecropping

A system of agriculture in which a landowner allows a tenant to use the land in return for a share of the crops produced on their portion of land.

Gang Labor

A system of labor, often used on plantations, where enslaved people were grouped into units or gangs for work, typically in agriculture.

Farm Prices

This term generally refers to the cost or price levels of agricultural products and commodities, which can significantly affect the economy.

Sharecropping Contract

An agricultural system prevalent after the Civil War where landowners allowed tenants to use the land in return for a portion of the crops produced on their portion of land.