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:

Abduction

The action of moving a limb or different body part away from the body's central axis or away from another body part.

Adduction

The movement of a body part toward the central axis of the body.

Circumduction

A circular movement of a limb or eye that combines flexion, extension, abduction, and adduction.

Rotation

The action or process of rotating on or as if on an axis or center, commonly used to describe the movement of celestial bodies or mechanical parts.