Suppose that a guitar string is plucked such that the center of the string is initially displaced 10 mm and then vibrates under damped harmonic motion. The note produced has a frequency of 110 Hz . The note is no longer audible to a normal human ear once the displacement at the middle of the string is less than 0.1 mm . What is the damping factor if the sound is no longer audible after 2.5 sec ? Round to 2 decimal places.
Suppose that a guitar string is plucked such that the center of the string is initially displaced 10 mm and then vibrates under damped harmonic motion. The note produced has a frequency of 110 Hz . The note is no longer audible to a normal human ear once the displacement at the middle of the string is less than 0.1 mm . What is the damping factor if the sound is no longer audible after 2.5 sec ? Round to 2 decimal places.
Solution Summary: The author explains how to calculate the damping factor if the sound is no longer audible after 2.5 sec.
Suppose that a guitar string is plucked such that the center of the string is initially displaced
10
mm
and then vibrates under damped harmonic motion. The note produced has a frequency of
110
Hz
. The note is no longer audible to a normal human ear once the displacement at the middle of the string is less than
0.1
mm
. What is the damping factor if the sound is no longer audible after
2.5
sec
? Round to
2
decimal places.
Can you answer this question and give step by step and why and how to get it. Can you write it (numerical method)
Can you answer this question and give step by step and why and how to get it. Can you write it (numerical method)
There are three options for investing $1150. The first earns 10% compounded annually, the second earns 10% compounded quarterly, and the third earns 10% compounded continuously. Find equations that model each investment growth and
use a graphing utility to graph each model in the same viewing window over a 20-year period. Use the graph to determine which investment yields the highest return after 20 years. What are the differences in earnings among the three
investment?
STEP 1: The formula for compound interest is
A =
nt
= P(1 + − − ) n²,
where n is the number of compoundings per year, t is the number of years, r is the interest rate, P is the principal, and A is the amount (balance) after t years. For continuous compounding, the formula reduces to
A = Pert
Find r and n for each model, and use these values to write A in terms of t for each case.
Annual Model
r=0.10
A = Y(t) = 1150 (1.10)*
n = 1
Quarterly Model
r = 0.10
n = 4
A = Q(t) = 1150(1.025) 4t
Continuous Model
r=0.10
A = C(t) =…
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