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

question 221

Multiple Choice

Solve the problem.
-The position(in feet) of an object oscillating up and down at the end of a spring is given by s $= \mathrm { A } \sin \left( \sqrt { \frac { \mathrm { k } } { \mathrm { m } } } \mathrm { t } \right)$ at time $t$ (in seconds) . The value of $\mathrm { A }$ is the amplitude of the motion, $\mathrm { k }$ is a measure of the stiffness of the spring, and $m$ is the mass of the object. Find the object's velocity at time $t$ .

• A) \(v = A \cos \left( \sqrt { \frac { k } { m } } t \right) \mathrm { ft } / \mathrm { sec }\)
• B) \(v = A \sqrt { \frac { \mathrm { k } } { \mathrm { m } } } \cos \left( \sqrt { \frac { \mathrm { k } } { \mathrm { m } } } \mathrm { t } \right) \mathrm { ft } / \mathrm { sec }\)
• C) \(v = - A \sqrt { \frac { k } { m } } \cos \left( \sqrt { \frac { k } { m } } t \right) \mathrm { ft } / \mathrm { sec }\)
• D) \(v = A \sqrt { \frac { \mathrm { m } } { \mathrm { k } } } \cos \left( \sqrt { \frac { \mathrm { k } } { \mathrm { m } } } \mathrm { t } \right) \mathrm { ft } / \mathrm { sec }\)

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