Suppose a Damping Force Affects the Vibration of a Spring $y = e ^ { - 8 t } ( \cos 2 t + 9 \sin 2 t )$

question 91

Multiple Choice

Suppose a damping force affects the vibration of a spring so that the displacement of the string is given by $y = e ^ { - 8 t } ( \cos 2 t + 9 \sin 2 t )$ . Find the average value of $y$ on the interval from $t = 0$ to $t = \pi$ . Round your answer to three decimal places.

• A) \(0.406\)
• B) \(0.131\)
• C) \(0.122\)
• D) \(0.129\)
• E) \(0.382\)

---

Definitions:

Check Register

A record, often part of a checkbook, that allows individuals to track checks written, deposits made, and current balances.

ATM

An Automated Teller Machine, a banking terminal that allows customers to perform financial transactions, such as cash withdrawals and deposits, without the need for a human cashier.

Debit

To deduct, to charge; a charge added to existing balance.

Personal Identification Number

A unique numerical code used in securing access to accounts or systems, often a password or security measure.