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hoa [83]
3 years ago
13

An object in simple hormonic motion starts at Amplitude Ao. Due to dampening, after 30 sec, the object is now at 30% of its orig

inal amplitude. What is the dampening constant of this system? A. 11s B. 25s C. 33s D. 84s E. 55s
Physics
1 answer:
Nookie1986 [14]3 years ago
4 0

Answer:

C ) 33 s.

Explanation:

In simple harmonic motion damping of amplitude  is logarithmic which is expressed as follows

A=A_0e^{-\frac{-b}{t}

A/A₀ = .3 (given ) , b is damping constant and t is time which is 30 s here.

.3 = e^\frac{-b}{t}

ln .3 = -b / 30

1.2 = b / 30

b = 36 s 0r 33 s

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y_{o}=1.96 m is the initial height of the cannonball

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t=0.63 s (5)

Substituting (5) in (1):

x=(23 m/s) cos(0\°) 0.63 s (6)

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x=14.49 m

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