A weight is attached to a spring suspended vertically from a ceiling.When a driving force is applied to the system, the weight moves vertically from its equilibrium position, and this motion is modeled by
$y = \frac { 1 } { 8 } \sin 2 t + \frac { 1 } { 6 } \cos 2 t$ where y is the distance from equilibrium (in feet) and t is the time (in seconds).
Find the amplitude of the oscillations of the weight.

A) $\frac { 1 } { 24 } \mathrm { ft }$
B) $\frac { 1 } { 10 } \mathrm { ft }$
C) $\frac { 5 } { 24 } \mathrm { ft }$
D) $\frac { 1 } { 5 } \mathrm { ft }$
E) $\frac { 24 } { 5 } \mathrm { ft }$

Question

A weight is attached to a spring suspended vertically from a ceiling.When a driving force is applied to the system, the weight moves vertically from its equilibrium position, and this motion is modeled by 
 $y = \frac { 1 } { 8 } \sin 2 t + \frac { 1 } { 6 } \cos 2 t$ where y is the distance from equilibrium (in feet) and t is the time (in seconds).
Find the amplitude of the oscillations of the weight.
 
A) $\frac { 1 } { 24 } \mathrm { ft }$
B) $\frac { 1 } { 10 } \mathrm { ft }$
C) $\frac { 5 } { 24 } \mathrm { ft }$
D) $\frac { 1 } { 5 } \mathrm { ft }$
E) $\frac { 24 } { 5 } \mathrm { ft }$

Quizplus · Accepted Answer

The amplitude of the oscillations is found by calculating the square root of the sum of the squares of the coefficients of the sine and cosine terms: $\sqrt{\left(\frac{1}{8}\right)^2 + \left(\frac{1}{6}\right)^2} = \sqrt{\frac{1}{64} + \frac{1}{36}} = \sqrt{\frac{9}{576} + \frac{16}{576}} = \sqrt{\frac{25}{576}} = \frac{5}{24}$ ft.

A Weight Is Attached to a Spring Suspended Vertically from a Ceiling.When