The amplitude of a lightly damped oscillator decreases by 3.0% during each cycle. What percentage of...
The amplitude of a lightly damped oscillator decreases by 3.0% during each cycle. What percentage of the mechanical energy of the oscillator is lost in each cycle?
A. 33%
B. 0.33%
C. 6%
D. 3%
E. 9%
Homework Answers
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The amplitude of a lightly damped oscillator decreases by 3.0%
during each cycle. What percentage of...
An oscillator has a period of 2.5 s. Its amplitude decreases by 7% during each cycle....
An oscillator has a period of 2.5 s. Its amplitude decreases by 7% during each cycle. (a) By how much does its energy decrease during each cycle? % (b) What is the time constant τ? (c) What is the Q factor?
9. Show that a lightly damped vibrator loses about 2πΟ of its energy in one cycle...
9. Show that a lightly damped vibrator loses about 2πΟ of its energy in one cycle of period T Hint: Consider the difference in the maximum potential energy of an oscillator at time 0 and time HT. The fraction of energy (E) lost is (E(-0)-E( TE-0
A damped harmonic oscillator consists of a block of mass 5kg and a spring with spring...
A damped harmonic oscillator consists of a block of mass 5kg and a spring with spring constant k = 10 N/m. Initially, the system oscillates with an amplitude of 63 cm. Because of the damping, the amplitude decreases by 56% of its initial value at the end of four oscillations. What is the value of the damping constant, b? What percentage of initial energy has been lost during these four oscillations?
A damped harmonic oscillator loses 8 percent of its mechanical energy per cycle. (a) By what...
A damped harmonic oscillator loses 8 percent of its mechanical energy per cycle. (a) By what percentage does its frequency differ from the natural frequency f0 = (1/2?)?k/m?
A damped oscillator loses 2.0% of its energy during each cycle. (a) How many cycles elapse...
A damped oscillator loses 2.0% of its energy during each cycle. (a) How many cycles elapse before half of its original energy is dissipated? (Use the 2.0% information to get a relation between γ and T, then use that to find t1/2 in terms of T) (b) What is its Q factor? (c) If the natural frequency is 150 Hz, what is the width of the resonance curve (in rad/s) when a sinusoidal force drives the oscillator?
(1) A damped oscillator has a quality factor of 20. Part A:- By what fraction does...
(1) A damped oscillator has a quality factor of 20. Part A:- By what fraction does the energy decrease during each cycle? Part B:- By what percentage does the damped angular frequency ωd differ from the undamped angular frequency?
A damped harmonic oscillator consists of a block (m = 3.00 kg), a spring (k =...
A damped harmonic oscillator consists of a block (m = 3.00 kg), a spring (k = 11.1 N/m), and a damping force (F = -bv). Initially, it oscillates with an amplitude of 28.7 cm; because of the damping, the amplitude falls to 0.760 of the initial value at the completion of 6 oscillations. (a) What is the value of b? (Hint: Assume that b2 << km.) (b) How much energy has been lost during these 6 oscillations?
Problem 15. (20 pts) Consider a damped driven oscillator with the following parameters s-100 N/m b=0.5kg/s...
Problem 15. (20 pts) Consider a damped driven oscillator with the following parameters s-100 N/m b=0.5kg/s m= 1 kg Fo=2N A) Find the resonant frequency, w. B) Find the damping rate y C) What is the quality factor Q for this oscillator? D) Is this oscillator lightly damped, critically damped, or heavily damped? E) Find the steady state amplitude when the oscillator is driven on resonance (Ω=w). F) Find the steady state amplitude when Ω_w+γ/2. G) Find the average power...
A damped oscillator has a frequency w’ that is 10% less than its undamped frequency. (a)...
A damped oscillator has a frequency w’ that is 10% less than its undamped frequency. (a) By what factor is the amplitude of the oscillation decreased during each oscillation? (b) By what factor is its energy reduced during each oscillation
Name: A simple harmonic oscillator has a period of oscillation of 0.33 s. What is the...
Name: A simple harmonic oscillator has a period of oscillation of 0.33 s. What is the frequency of the 1. oscillator? a. 0.053 Hz b. 0.33 Hz c. 2.1 Hz d. 3.0 Hz e. 19 Hz
9. Show that a lightly damped vibrator loses about 2πΟ of its energy in one cycle of period T Hint: Consider the difference in the maximum potential energy of an oscillator at time 0 and time HT. The fraction of energy (E) lost is (E(-0)-E( TE-0
Problem 15. (20 pts) Consider a damped driven oscillator with the following parameters s-100 N/m b=0.5kg/s m= 1 kg Fo=2N A) Find the resonant frequency, w. B) Find the damping rate y C) What is the quality factor Q for this oscillator? D) Is this oscillator lightly damped, critically damped, or heavily damped? E) Find the steady state amplitude when the oscillator is driven on resonance (Ω=w). F) Find the steady state amplitude when Ω_w+γ/2. G) Find the average power...
Name: A simple harmonic oscillator has a period of oscillation of 0.33 s. What is the frequency of the 1. oscillator? a. 0.053 Hz b. 0.33 Hz c. 2.1 Hz d. 3.0 Hz e. 19 Hz
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