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

question 137

Multiple Choice

Solve the problem.
-The position (in centimeters) of an object oscillating up and down at the end of a spring is given by $s = A \sin \left( \sqrt { \frac { k } { m } } t \right)$ at time $t$ (in seconds) . The value of A is the amplitude of the motion, $k$ is a measure of the stiffness of the spring, and $m$ is the mass of the object. How fast is the object moving when it is moving fastest?

• A) \(A \sqrt { \frac { \mathrm { m } } { \mathrm { k } } } \mathrm { cm } / \mathrm { sec }\)
• B) \(\sqrt { \frac { \mathrm { k } } { \mathrm { m } } } \mathrm { cm } / \mathrm { sec }\)
• C) \(\mathrm { A } \mathrm { cm } / \mathrm { sec }\)
• D) \(A \sqrt { \frac { \mathrm { k } } { \mathrm { m } } } \mathrm { cm } / \mathrm { sec }\)

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Definitions:

Adequate Physical Space

Sufficient area or environment that meets the needs of an activity or the individuals involved, allowing for comfort and functionality.

Intramuscular Dose

A method of administering medication directly into a muscle, allowing for quick absorption into the bloodstream.

Increasingly More Aggressive

Becoming progressively more forceful, hostile, or assertive in behavior or attitudes.

Startle Reactions

The automatic, rapid response of the body to a sudden, unexpected stimulus, usually perceived as potentially threatening.