Solve the Problem $\mathrm { s } ( \mathrm { t } ) = \sin \sqrt { \frac { \mathrm { k } } { \mathrm { m } } } \mathrm { t }$

question 53

Multiple Choice

Solve the problem.
-The formula for the up and down motion of a weight on a spring is given by $\mathrm { s } ( \mathrm { t } ) = \sin \sqrt { \frac { \mathrm { k } } { \mathrm { m } } } \mathrm { t }$ . If the spring constant is 5 , then what mass $m$ must be used in order to produce a period of 6 seconds?

• A) \(\frac { 5 \pi } { 2 }\)
• B) \(\frac { 2 \pi } { 5 }\)
• C) \(\frac { 45 } { \pi ^ { 2 } }\)
• D) \(\frac { 4 } { \pi ^ { 2 } }\)

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Definitions:

Endowment

The total resources available to an individual or institution, including assets, capabilities, and financial means.

General Equilibrium Analysis

A method in economics that attempts to understand how supply and demand interact across multiple markets simultaneously, and how they reach a state of balance.

Feasible Allocation

In economics, it refers to the distribution of resources or goods in such a manner that it is possible given the available supply.

Second Welfare Theorem

An economic principle stating that under certain conditions, any efficient allocation of resources can be attained through a competitive equilibrium, assuming perfect markets and price flexibility.