Solve the Problem $S = 2 \sin \left( \frac { \sqrt { \mathrm { k } } } { \mathrm { m } } \right) \mathrm { t }$

question 189

Multiple Choice

Solve the problem.
-A formula for the up-and-down motion of a weight on a spring is given by $S = 2 \sin \left( \frac { \sqrt { \mathrm { k } } } { \mathrm { m } } \right) \mathrm { t }$ , where $\mathrm { k }$ is the spring constant, $\mathrm { m }$ is the mass, and $\mathrm { t }$ is the time. Solve the equation for $\mathrm { t }$ .

• A) \(t = \frac { m } { \sqrt { k } } \arcsin \left( \frac { s } { 2 } \right)\)
• B) \(t = \frac { \sqrt { \mathrm { k } } } { \mathrm { m } } \sin \left( \frac { 2 } { \mathrm {~S} } \right)\)
• C) \(t = \frac { \sqrt { \mathrm { k } } } { \mathrm { m } } \arcsin \left( \frac { \mathrm { s } } { 2 } \right)\)
• D) \(t = \frac { \mathrm { m } } { \sqrt { \mathrm { k } } } \sin \left( \frac { \mathrm { S } } { 2 } \right)\)

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Definitions:

Sensitivity Analysis

A technique used to determine how different values of an independent variable impact a particular dependent variable under a given set of assumptions.

Input

Resources such as raw materials, labor, and energy used in the production process to produce outputs, or goods and services.

Present Value Factors

Multipliers used in calculating the present value of future cash flows, reflecting the time value of money.

Compound Interest

Interest calculated on the initial principal, which also includes all of the accumulated interest from previous periods on a deposit or loan.