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1. Consider a weakly-damped, driven SHO. Show that the driving frequency for which the steady-state amplitude...
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...
Problem 17. A) In steady state, does a damped, driven oscillator oscillate at the frequency of...
Problem 17. A) In steady state, does a damped, driven oscillator oscillate at the frequency of the driving force, the natural frequency of the oscillator or neither of these frequencies? B) Ella Fitzgerald could break a wine glass with her voice but Louis Armstrong could not. Is this likely because Ella could sing louder than Louis? Justify your answer. C) What happens to the width of the average-power-delivered vs driving frequency curve if the damping is increased? D) What happens...
A driving force of the form F(t) = (0.212 N) sin (2xft) acts on a weakly...
A driving force of the form F(t) = (0.212 N) sin (2xft) acts on a weakly damped spring oscillator with mass 6.98 kg, spring constant 362 N/m, and damping constant 0.261 kg/s. What frequency fo of the driving force will maximize the response of the oscillator? fo = Hz Find the amplitude Ao of the oscillator's steady-state motion when the driving force has this frequency Find the amplitude Ap of the oscillator's steady-state motion when the driving force has this...
ineers can determine properties of a structure that is modeled as damped spring oscillator-such as a...
ineers can determine properties of a structure that is modeled as damped spring oscillator-such as a bridge-by applying a driving force to it. A weakly damped spring oscillator of mass 0.242 kg is driven by a sinusoidal force at the oscillator's resonance frequency of 34.0 Hz. Find the value of the spring constant Number N/ m The amplitude of the driving force is 0.471 N and the amplitude of the oscillator's steady-state motion in response to this driving force is...
. Consider a weakly damped oscillator that is being driven by the periodic rectangular pulses sho...
. Consider a weakly damped oscillator that is being driven by the periodic rectangular pulses shown in the following figure. Let the natural period of the oscillator beTo-3 and the damping constant be β = 0.1. Let the pulse last for a time Δτ= 1.5 and have a height fmax -5. Calculate the first four Fourier coefficient An for the long-term motion x(t) of the oscillator, assuming that the relation between the drive period τ and the natural period τοΒ...
Chapter 31, Problem 038 The current amplitude 1 versus driving angular frequency ad for a driven...
Chapter 31, Problem 038 The current amplitude 1 versus driving angular frequency ad for a driven RLC circuit is given in the figure, where the vertical axis scale is set by Is-4.11 A. The inductance is 213 μΗ, and the emf amplitude is 9.1 V. What are (a)Cand (b)R? 0 1o 30 50 (1000 rad/s) (a) Number Units (b) Number Units
2. Resonant Frequency. Show that the resonant frequency of a driven (forced) DHO is: Note that...
2. Resonant Frequency. Show that the resonant frequency of a driven (forced) DHO is: Note that this expression strongly resembles the "natural frequency" of the DHO, but it is not the same. The "2" is different. (Hint: take the first derivative of the amplitude A(o) of the particular solution, F/G(o), with respect to ω, and set this equal to zero. Pay special attention to the inner derivative. Simple algebra will then yield the result.) 1S
A simple damped mechanical harmonic oscillator with damping constant γ is driven by a force ?0?????....
A simple damped mechanical harmonic oscillator with damping constant γ is driven by a force ?0?????. Show that the FWHM of the amplitude A(ω) vs. angular frequency ω curve is ?√3. You can assume that Q>>1 and ω is very close to ω0. Formulae in the book can be used. But you will have to reference the page and equation number.
3. A damped harmonic oscillator is driven by an external force of the form mfo sin...
3. A damped harmonic oscillator is driven by an external force of the form mfo sin ot. The equation of motion is therefore x + 2ßx + ω x-fo sin dot. carefully explaining all steps, show that the steady-state solution is given by x(t) A() sin at 8) Find A (a) and δ(w).
A damped oscillator with natural frequency wo and damping K is driven by a period square...
A damped oscillator with natural frequency wo and damping K is driven by a period square wave force with amplitude A such that F(t)= A Find the Fourier series for F(t), and solve for the amplitude of the motion of the oscillator. For which frequency wn is the resonance condition the most closely satisfied? Plot the maximum amplitude (in units of A) as a function of wn for the conditions with the spring constant k 1, m 2, K 0.1,...
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...
Problem 17. A) In steady state, does a damped, driven oscillator oscillate at the frequency of the driving force, the natural frequency of the oscillator or neither of these frequencies? B) Ella Fitzgerald could break a wine glass with her voice but Louis Armstrong could not. Is this likely because Ella could sing louder than Louis? Justify your answer. C) What happens to the width of the average-power-delivered vs driving frequency curve if the damping is increased? D) What happens...
A driving force of the form F(t) = (0.212 N) sin (2xft) acts on a weakly damped spring oscillator with mass 6.98 kg, spring constant 362 N/m, and damping constant 0.261 kg/s. What frequency fo of the driving force will maximize the response of the oscillator? fo = Hz Find the amplitude Ao of the oscillator's steady-state motion when the driving force has this frequency Find the amplitude Ap of the oscillator's steady-state motion when the driving force has this...
ineers can determine properties of a structure that is modeled as damped spring oscillator-such as a bridge-by applying a driving force to it. A weakly damped spring oscillator of mass 0.242 kg is driven by a sinusoidal force at the oscillator's resonance frequency of 34.0 Hz. Find the value of the spring constant Number N/ m The amplitude of the driving force is 0.471 N and the amplitude of the oscillator's steady-state motion in response to this driving force is...
. Consider a weakly damped oscillator that is being driven by the periodic rectangular pulses shown in the following figure. Let the natural period of the oscillator beTo-3 and the damping constant be β = 0.1. Let the pulse last for a time Δτ= 1.5 and have a height fmax -5. Calculate the first four Fourier coefficient An for the long-term motion x(t) of the oscillator, assuming that the relation between the drive period τ and the natural period τοΒ...
Chapter 31, Problem 038 The current amplitude 1 versus driving angular frequency ad for a driven RLC circuit is given in the figure, where the vertical axis scale is set by Is-4.11 A. The inductance is 213 μΗ, and the emf amplitude is 9.1 V. What are (a)Cand (b)R? 0 1o 30 50 (1000 rad/s) (a) Number Units (b) Number Units
2. Resonant Frequency. Show that the resonant frequency of a driven (forced) DHO is: Note that this expression strongly resembles the "natural frequency" of the DHO, but it is not the same. The "2" is different. (Hint: take the first derivative of the amplitude A(o) of the particular solution, F/G(o), with respect to ω, and set this equal to zero. Pay special attention to the inner derivative. Simple algebra will then yield the result.) 1S
3. A damped harmonic oscillator is driven by an external force of the form mfo sin ot. The equation of motion is therefore x + 2ßx + ω x-fo sin dot. carefully explaining all steps, show that the steady-state solution is given by x(t) A() sin at 8) Find A (a) and δ(w).
A damped oscillator with natural frequency wo and damping K is driven by a period square wave force with amplitude A such that F(t)= A Find the Fourier series for F(t), and solve for the amplitude of the motion of the oscillator. For which frequency wn is the resonance condition the most closely satisfied? Plot the maximum amplitude (in units of A) as a function of wn for the conditions with the spring constant k 1, m 2, K 0.1,...
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