The displacement from equilibrium of an oscillating weight suspended by a spring is given by $y ( t ) = \frac { 1 } { 4 } \cos ( 6 t )$ , where y is the displacement (in feet) and t is the time (in seconds).Find the displacements when $t = 5$ .(Round your answers to two decimal places.)

A) $y ( 5 ) \approx 0.04$ foot
B) $y ( 5 ) \approx 0.14$ foot
C) $y ( 5 ) \approx 0.44$ foot
D) $y ( 5 ) \approx 0.34$ foot
E) $y ( 5 ) \approx 0.24$ foot

Question

The displacement from equilibrium of an oscillating weight suspended by a spring is given by $y ( t ) = \frac { 1 } { 4 } \cos ( 6 t )$ , where y is the displacement (in feet) and t is the time (in seconds).Find the displacements when $t = 5$ .(Round your answers to two decimal places.)
 
A) $y ( 5 ) \approx 0.04$ foot
B) $y ( 5 ) \approx 0.14$ foot
C) $y ( 5 ) \approx 0.44$ foot
D) $y ( 5 ) \approx 0.34$ foot
E) $y ( 5 ) \approx 0.24$ foot

Quizplus · Accepted Answer

To find the displacement at $t = 5$, substitute $t = 5$ into the given equation: $y(5) = \frac{1}{4} \cos(6 \times 5) = \frac{1}{4} \cos(30)$. Calculating this gives $y(5) \approx 0.04$ foot.

The Displacement from Equilibrium of an Oscillating Weight Suspended by a Spring