in a science museum, a 110kg brass pendulum bob swings at theend of a 15.0m long

Question

in a science museum, a 110kg brass pendulum bob swings at theend of a 15.0m long wire. the pendulum is started at exactly 8:00am every morning by pulling it 1.5m to the side and releasing it.because of its compact shape and smooth surface, the pendulum'sdamping constant is only 0.010kg/s. at exactly 12:00 noon, how manyoscillations will the pendulum have completed and what is itsamplitude? the answer is 1853 oscillations and 0.780m for amplitude I don't know how to solve this problem...please help! in a science museum, a 110kg brass pendulum bob swings at theend of a 15.0m long wire. the pendulum is started at exactly 8:00am every morning by pulling it 1.5m to the side and releasing it.because of its compact shape and smooth surface, the pendulum'sdamping constant is only 0.010kg/s. at exactly 12:00 noon, how manyoscillations will the pendulum have completed and what is itsamplitude? the answer is 1853 oscillations and 0.780m for amplitude I don't know how to solve this problem...please help!

Explanation / Answer

the time period of the pendulum is T = 2 * (l/g)1/2 l = 15.0 m and g = 9.8 m/s2 or T = 2 * (15.0/9.8)1/2 = 2 * 3.14 * 1.237 =7.76 s the pendulum makes oscillations for a time t = 4 hours = 4 *60 * 60 s = 14400 s the number of oscillations the pendulum have completedis N = (t/T) = (14400/7.76) = 1855 oscillations the amplitude of the oscillations is x = A * e-(b/2m)t * cos(wt + ) A = 1.5 m,b = 0.010 kg/s,m = 110 kg,w = (2/T) and = 0 or x = 1.5 * e-(0.010/2 * 110) * 14400 *cos((2/14400) + 0) or x = 1.5 * e-(0.010/2 * 110) * 14400 *cos((/7200)) or x = 0.845 m or T = 2 * (15.0/9.8)1/2 = 2 * 3.14 * 1.237 =7.76 s the pendulum makes oscillations for a time t = 4 hours = 4 *60 * 60 s = 14400 s the number of oscillations the pendulum have completedis N = (t/T) = (14400/7.76) = 1855 oscillations the amplitude of the oscillations is x = A * e-(b/2m)t * cos(wt + ) A = 1.5 m,b = 0.010 kg/s,m = 110 kg,w = (2/T) and = 0 or x = 1.5 * e-(0.010/2 * 110) * 14400 *cos((2/14400) + 0) or x = 1.5 * e-(0.010/2 * 110) * 14400 *cos((/7200)) or x = 0.845 m

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.