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**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[tex]_{}0[/tex] e [tex]^{}-(b/2m)t[/tex] cos( [tex]\varpi[/tex] [tex]\acute{}[/tex] t+[tex]\phi[/tex])

I used the first bit of the equation to find the exact amplitude t(x) when x=14400 (x=A[tex]_{}0[/tex]e[tex]^{}-(b/2m)t[/tex] 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 ([tex]\varpi\acute{}[/tex]) and multiplied that by the number of seconds (14400), but the resulting answer was incorrect. Since [tex]\phi[/tex]=0, taking the cosine of ([tex]\varpi\acute{}[/tex]) 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.

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