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:

Isotope

Forms of a specific chemical element distinguished by having identical proton counts yet varying quantities of neutrons within their cores.

Neutrons

Subatomic particles found in the nucleus of an atom with no electric charge.

Protons

Subatomic particles found in the nucleus of an atom, carrying a positive electrical charge.

Isotope

Isotopes are variants of a particular chemical element which differ in neutron number, and consequently in nucleon number, but have the same number of protons in their atomic nuclei.