Question

The motion of an underdamped oscillator is described by equation x=Ae−(b/2m)tcos(ω′t+ϕ). Let the phase angle ϕ be zero.

Part A

According to this equation, what is the value of x at t=0?

Express your answer in terms of the variables A, b, m, ω, and ϕ.

x(0) =

A

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Correct

Part B

What is the magnitude of the velocity at t=0?

Express your answer in terms of the variables A, b, m, ω, and ϕ.

vx(0) =

b2mA

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Correct

Part C

What is the direction of the velocity at t=0?

What is the direction of the velocity at ?

positive

negative

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Correct

Part D

What does the result tell you about the slope of the graph of x versus t near t=0?

Essay answers are limited to about 500 words (3800 characters maximum, including spaces).

3800 Character(s) remaining

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Part E

Obtain an expression for the acceleration axat t=0.

Express your answer in terms of the variables A, b, m, ω, and ϕ.

ax=

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Part F

For what value or range of values of the damping constant b (in terms of k and m) is the acceleration at t=0 negative, zero, and positive?

Check all that apply.

Check all that apply.

zero if b=km−−−√

negative if b>2km−−−−√

negative if b<km−−−√

positive if b>2km−−−−√

negative if b<2km−−−−√

positive if b<2km−−−−√

negative if b>km−−−√

positive if b>km−−−√

positive if b<km−−−√

zero if b=2km−−−−√

Answer 1