A metal block with a mass of 4.00 kg oscillates at the end of a vertical spring with a spring constant of 2.80 x 10 N/m. The motion is damped by air resistance, and the damping coefficient is b = 3.00 N - s/m. (a) What is the frequency (in Hz) of the damped oscillation? 13.3 Hz (b) By what percentage does the amplitude of the oscillation decrease in each cycle? 2.8 % (c) Over what time interval (in s) does the energy of the system drop to 5.00% of its initial value? 3.99 S

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1.9
A metal block with a mass of 4.00 kg oscillates at the end of a vertical spring with a spring constant of 2.80 x 104 N/m. The
motion is damped by air resistance, and the damping coefficient is b = 3.00 N. s/m.
(a) What is the frequency (in Hz) of the damped oscillation?
13.3
Hz
(b) By what percentage does the amplitude of the oscillation decrease in each cycle?
2.8
%
(c) Over what time interval (in s) does the energy of the system drop to 5.00% of its initial value?
3.99
S
(d) What If? The atmosphere of Venus is 50 times thicker than that on Earth. If the effect of air resistance on Venus is
represented by b= 150 N s/m, recalculate the answers for parts (a) to (c) for this system if it is set in motion in the
atmosphere of Venus.
What is the frequency (in Hz) of the damped oscillations?
81.54
x
Follow the same steps as in part (a), only use the new value of b. Hz
What is the percentage decrease in amplitude in each cycle?
14.1
X
Follow the same steps as in part (b), only use the new value of b. Remember the angular frequency has now changed
as well. Be sure to express your answer as a percentage, and not a fraction. %
What is the time interval (in s) for the energy to drop to 5.00% of its initial value?
0.08
S
Transcribed Image Text:1.9 A metal block with a mass of 4.00 kg oscillates at the end of a vertical spring with a spring constant of 2.80 x 104 N/m. The motion is damped by air resistance, and the damping coefficient is b = 3.00 N. s/m. (a) What is the frequency (in Hz) of the damped oscillation? 13.3 Hz (b) By what percentage does the amplitude of the oscillation decrease in each cycle? 2.8 % (c) Over what time interval (in s) does the energy of the system drop to 5.00% of its initial value? 3.99 S (d) What If? The atmosphere of Venus is 50 times thicker than that on Earth. If the effect of air resistance on Venus is represented by b= 150 N s/m, recalculate the answers for parts (a) to (c) for this system if it is set in motion in the atmosphere of Venus. What is the frequency (in Hz) of the damped oscillations? 81.54 x Follow the same steps as in part (a), only use the new value of b. Hz What is the percentage decrease in amplitude in each cycle? 14.1 X Follow the same steps as in part (b), only use the new value of b. Remember the angular frequency has now changed as well. Be sure to express your answer as a percentage, and not a fraction. % What is the time interval (in s) for the energy to drop to 5.00% of its initial value? 0.08 S
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