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, which is $\sqrt{\left(\frac{1}{8}\right)^2 + \left(\frac{1}{6}\right)^2} = \frac{5}{24}$ ft.

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