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

question 29

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 $\mathrm { A } = 0.39 \mathrm {~m}$ and $\mathrm { L } = 0.49 \mathrm {~m}$ . Round all answers to the nearest hundredth.

• A) \(0.70 \mathrm { sec } , 0.39 \mathrm {~m} , - 0.70\) units to the left
• B) \(1.41 \mathrm { sec } , 0.39 \mathrm {~m} , 0.35\) units to the right
• C) \(0.31 \mathrm { sec } , 0.39 \mathrm {~m} , - 0.079\) units to the left
• D) \(1.41 \mathrm { sec } , 0.39 \mathrm {~m} , - 0.35\) units to the left

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Definitions:

9-Year

An undefined term likely referring to a period or duration of nine years.

Compounded Quarterly

This refers to the process where interest is calculated and added to the principal sum of an investment or loan on a quarterly basis.

12%

A representation of twelve parts in a hundred, often used to describe interest rates, growth percentages, or discounts.

3 Years

A period or duration of three calendar years.