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(a) A device consists of an object with a weight of 35.0 N hanging vertically from a spring with a spring constant of 250 N/m. There is negligible damping of the oscillating system. Applied to the system is a harmonic driving force of 13.0 Hz, which causes the object to oscillate with an amplitude of 3.00 cm. What is the maximum value of the driving force (in N)? (Enter the magnitude.) 706.33 N (b) What If? The device is altered so that there is a damping coefficient of b = 5.00 N s/m. The hanging weight and spring constant remain the same. The same driving force as found in part (a) is applied with the same frequency. What is the new amplitude (in cm) of oscillation? 1.74 X Use the expression for amplitude you used in part (a). Compute the values, individually, of the two squared terms in the square root in the denominator of the expression for amplitude. How do they compare to each other? Is the term with the damping coefficient significant compared to the other? cm (c) What If? Repeat the same calculation as part (b), only now with a damping coefficient of b = 100 N s/m. (Enter the answer in cm.) 0.1 Use the expression for amplitude you used in part (a). Compute the values, individually, of the two squared terms in the square root in the denominator of the expression for amplitude. How do they compare to each other now? Will the damping now have a significant effect? Be careful with squares and square roots. cm

(a) A device consists of an object with a weight of 35.0 N hanging vertically from a spring with a spring constant of 250 N/m. There is negligible damping of the oscillating system. Applied to the system is a harmonic driving force of 13.0 Hz, which causes the object to oscillate with an amplitude of 3.00 cm. What is the maximum value of the driving force (in N)? (Enter the magnitude.) 706.33 N (b) What If? The device is altered so that there is a damping coefficient of b = 5.00 N s/m. The hanging weight and spring constant remain the same. The same driving force as found in part (a) is applied with the same frequency. What is the new amplitude (in cm) of oscillation? 1.74 X Use the expression for amplitude you used in part (a). Compute the values, individually, of the two squared terms in the square root in the denominator of the expression for amplitude. How do they compare to each other? Is the term with the damping coefficient significant compared to the other? cm (c) What If? Repeat the same calculation as part (b), only now with a damping coefficient of b = 100 N s/m. (Enter the answer in cm.) 0.1 Use the expression for amplitude you used in part (a). Compute the values, individually, of the two squared terms in the square root in the denominator of the expression for amplitude. How do they compare to each other now? Will the damping now have a significant effect? Be careful with squares and square roots. cm

Principles of Physics: A Calculus-Based Text
Principles of Physics: A Calculus-Based Text
5th Edition
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter12: Oscillatory Motion
Section: Chapter Questions
Problem 66P: Consider the damped oscillator illustrated in Figure 12.16a. The mass of the object is 375 g, the...
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(a) A device consists of an object with a weight of 35.0 N hanging vertically from a spring with a spring constant of 250 N/m. There is negligible damping of the oscillating system. Applied to the system is a harmonic driving force of 13.0 Hz, which causes the object to oscillate with an amplitude of 3.00 cm. What is the maximum value of the driving force (in N)? (Enter the magnitude.) 706.33 N (b) What If? The device is altered so that there is a damping coefficient of b = 5.00 N s/m. The hanging weight and spring constant remain the same. The same driving force as found in part (a) is applied with the same frequency. What is the new amplitude (in cm) of oscillation? 1.74 X Use the expression for amplitude you used in part (a). Compute the values, individually, of the two squared terms in the square root in the denominator of the expression for amplitude. How do they compare to each other? Is the term with the damping coefficient significant compared to the other? cm (c) What If? Repeat the same calculation as part (b), only now with a damping coefficient of b = 100 N s/m. (Enter the answer in cm.) 0.1 X Use the expression for amplitude you used in part (a). Compute the values, individually, of the two squared terms in the square root in the denominator of the expression for amplitude. How do they compare to each other now? Will the damping now have a significant effect? Be careful with squares and square roots. cm Need Help? Read It
Transcribed Image Text:(a) A device consists of an object with a weight of 35.0 N hanging vertically from a spring with a spring constant of 250 N/m. There is negligible damping of the oscillating system. Applied to the system is a harmonic driving force of 13.0 Hz, which causes the object to oscillate with an amplitude of 3.00 cm. What is the maximum value of the driving force (in N)? (Enter the magnitude.) 706.33 N (b) What If? The device is altered so that there is a damping coefficient of b = 5.00 N s/m. The hanging weight and spring constant remain the same. The same driving force as found in part (a) is applied with the same frequency. What is the new amplitude (in cm) of oscillation? 1.74 X Use the expression for amplitude you used in part (a). Compute the values, individually, of the two squared terms in the square root in the denominator of the expression for amplitude. How do they compare to each other? Is the term with the damping coefficient significant compared to the other? cm (c) What If? Repeat the same calculation as part (b), only now with a damping coefficient of b = 100 N s/m. (Enter the answer in cm.) 0.1 X Use the expression for amplitude you used in part (a). Compute the values, individually, of the two squared terms in the square root in the denominator of the expression for amplitude. How do they compare to each other now? Will the damping now have a significant effect? Be careful with squares and square roots. cm Need Help? Read It
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