Suppose a damping force affects the vibration of a spring so that the displacement of the string is given by .Find the average value of y on the interval from to .Round your answer to three decimal places.
A)1.125
B)0.318
C)0.286
D)0.358
E)0.900

Question

Suppose a damping force affects the vibration of a spring so that the displacement of the string is given by  .Find the average value of y on the interval from  to  .Round your answer to three decimal places. ​
A)1.125 
B)0.318 
C)0.286 
D)0.358 
E)0.900

Quizplus · Accepted Answer

To find the average value of y, we need to evaluate the definite integral of y from t = 0.153 to t = 1.786 and divide by the length of the interval (1.786 - 0.153). Using a calculator, we get:

(1/1.633) * ∫[0.153, 1.786] 11e^(-t/5) sin(5t + 1) dt ≈ 0.286

Therefore, the answer is (C) 0.286.

Suppose a Damping Force Affects the Vibration of a Spring