An object undergoing simple harmonic motion has a maximum displacement of $6.2 \mathrm {~m}$ at $t = 0.00 \mathrm {~s}$ If the angular frequency of oscillation is $1.6 \mathrm { rad } / \mathrm { s }$ what is the object's displacement when $t = 3.5 \mathrm {~s} ?$
A)4.8 m
B)5.6 m
C)3.7 m
D)3.1 m

Question

Quizplus · Accepted Answer

The object's displacement is given by $x = A \cos(\omega t)$, where $A$ is the maximum displacement, $\omega$ is the angular frequency, and $t$ is the time. At $t = 0.00 \mathrm {~s}$, the object is at its maximum displacement of $6.2 \mathrm {~m}$, so $A = 6.2 \mathrm {~m}$. The angular frequency is given as $1.6 \mathrm { rad } / \mathrm { s }$, so $\omega = 1.6 \mathrm { rad } / \mathrm { s }$. At $t = 3.5 \mathrm {~s}$, the object's displacement is given by:$$x = 6.2 \mathrm {~m} \cos(1.6 \mathrm { rad } / \mathrm { s } \times 3.5 \mathrm {~s}) = 4.8 \mathrm {~m}$$Therefore, the object's displacement when $t = 3.5 \mathrm {~s}$ is 4.8 m.

An Object Undergoing Simple Harmonic Motion Has a Maximum Displacement 6.2 m6.2 \mathrm {~m}6.2 m

An Object Undergoing Simple Harmonic Motion Has a Maximum Displacement $6.2 \mathrm {~m}$