A Spring with A $3 - \mathrm { kg }$ Mass Is Held Stretched

question 24

Multiple Choice

A spring with a $3 - \mathrm { kg }$ mass is held stretched $0.9 \mathrm {~m}$ beyond its natural length by a force of $30 \mathrm {~N}$ . If the spring begins at its equilibrium position but a push gives it an initial velocity of $1 \mathrm {~m} / \mathrm { s }$ , find the position $x ( t )$ of the mass after $t$ seconds.

• A)\(x ( t ) = 0.3 \sin \left( \frac { 10 } { 3 } t \right)\)
• B)\(x ( t ) = 0.4 \cos \left( \frac { 10 } { 3 } t \right)\)
• C) \(x ( t ) = 1 \sin ( 7 t )\)
• D)\(x ( t ) = 0.3 \sin \left( \frac { 10 } { 3 } t \right) + 0.4 \cos \left( \frac { 10 } { 3 } t \right)\)
• E) \(x ( t ) = \frac { 10 } { 3 } \sin ( 7 t )\)

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Definitions:

Nitrogen Atom

A chemical element with atomic number 7, essential to life on Earth, and a common element in organic compounds.

CNC Bond Angle

The angle formed between two carbon atoms and a nitrogen atom connected in a molecule.

Hybridization

The concept in molecular chemistry and physics that describes the mixing of atomic orbitals to form new hybrid orbitals suitable for the pairing of electrons to form chemical bonds.

Indicated Atom

An atom within a molecule highlighted or specified for discussion or analysis.