Solve the Problem $\mathrm { L }$ , When Displaced Horizontally and Released, Oscillates with Harmonic Motion

question 115

Multiple Choice

Solve the problem.
-A pendulum of length $\mathrm { L }$ , when displaced horizontally and released, oscillates with harmonic motion according to the equation $\mathrm { y } = \mathrm { A } \sin ( ( \sqrt { \mathrm { g } / \mathrm { L } } ) \mathrm { t } + \pi / 2 )$ , where $\mathrm { y }$ is the distance in meters from the rest position $t$ seconds after release, and $g = 9.8 \mathrm {~m} / \mathrm { sec } ^ { 2 }$ . Identify the period, amplitude, and phase shift when $\mathrm { A } = 0.28 \mathrm {~m}$ and $\mathrm { L } = 1.96 \mathrm {~m}$ . Round all answers to the nearest hundredth.

• A) \(1.40 \mathrm { sec } , 0.28 \mathrm {~m} , - 1.40\) units to the left
• B) \(2.80 \mathrm { sec } , 0.28 \mathrm {~m} , 0.70\) units to the right
• C) \(2.80 \mathrm { sec } , 0.28 \mathrm {~m} , - 0.70\) units to the left
• D) \(1.26 \mathrm { sec } , 0.28 \mathrm {~m} , - 0.314\) units to the left

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Definitions:

Biconditional

A logical statement of the form "if and only if", showing that both conditions must be true or both false.

Biconditionals

Statements that are true only if both components are either true or false together, often expressed as "if and only if."

Conjunction

In logic, an operator that connects two statements or propositions so that the resulting statement is true only if both components are true.

Disjunction

A logical operation yielding a true value if at least one of its operands is true.