# Damped Oscillation and amplitude

#### BAC5.2

1. Homework Statement

Given: "In a science museum, a 110 kg brass pendulum bob swings at the end of a 15.0-m-long wire. The pendulum is started at exactly 8:00 a.m. every morning by pulling it 1.5 m to the side and releasing it. Because of its compact shape and smooth surface, the pendulum's damping constant is only 0.010 kg/s."

Questions:

(1) At exactly 12:00 noon, how many oscillations will the pendulum have completed?

(2) And what is its amplitude?

2. Homework Equations

None Given

3. The Attempt at a Solution

I used the equation x=A$$_{}0$$ e $$^{}-(b/2m)t$$ cos( $$\varpi$$ $$\acute{}$$ t+$$\phi$$)

I used the first bit of the equation to find the exact amplitude t(x) when x=14400 (x=A$$_{}0$$e$$^{}-(b/2m)t$$ to find the amplitude)

But the trouble I'm having is the number of oscillations in the 4 hour period.

I took the angular frequency ($$\varpi\acute{}$$) and multiplied that by the number of seconds (14400), but the resulting answer was incorrect. Since $$\phi$$=0, taking the cosine of ($$\varpi\acute{}$$) gives another answer, but I'm not confident that it is the correct answer, and I don't want to stab in the dark until I get it right.

I'm a bit stuck.

Since this is damped oscillation, and the initial period is greater than one second, the number HAS to be less than 14400.

Any help? Am I on the right track? Is there something I'm missing?

Note: It doesn't seem that the latex is putting superscripts in the correct locations, so please bear with me.

Last edited:
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#### learningphysics

Homework Helper
have a look at the thread in intro physics.

#### BAC5.2

Thank you! All solved.

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