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Q.3 Consider a damped harmonic oscillator. After four cycles the amplitude of the oscillator has dropped...
2. The amplitude of a damped harmonic oscillator drops to 1/e of its initial value after...
2. The amplitude of a damped harmonic oscillator drops to 1/e of its initial value after n complete cycles. Show that the ratio of the period of oscillator to the period of the same oscillator with no damping is given by Td To when n is large.
1. The frequency of a damped harmonic oscillator is 100 Hz, and the ratio of the...
1. The frequency of a damped harmonic oscillator is 100 Hz, and the ratio of the amplitude of two successive maxima is one half. a. What is the natural (undamped) frequency of this oscillator, in Hertz? b. If the oscillator is launched at time t0 from the origin with speed 2 m/s, what is its speed at time t 0.0140 sec?
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 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?
7. (a) Explain what is meant by damped harmonic motion, and write down a differential equation describing this phenomenon b) Give an example of a damped harmonic oscillator in practice. Sketch the os...
7. (a) Explain what is meant by damped harmonic motion, and write down a differential equation describing this phenomenon b) Give an example of a damped harmonic oscillator in practice. Sketch the oscilla- tions it undergoes, and calculate their frequency and damping rate for a natural (undamped) frequency wo 10 Hz and damping coefficient γ-: 2.0 s-1
7. (a) Explain what is meant by damped harmonic motion, and write down a differential equation describing this phenomenon b) Give an example...
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 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.
58 For the damped oscillator system shown in Fig. 15-16, with m 250 g, k 85...
58 For the damped oscillator system shown in Fig. 15-16, with m 250 g, k 85 N/m, and b - 70 g/s, what is the ratio of the oscil- lation amplitude at the end of 20 cycles to the initial oscillation amplitude? Rigid support Springiness, k Mass m Vane Damping, b Figure 15-16 An idealized damped simple harmonic oscillator. A vane immersed in a liquid exerts a damping force on the block as the block oscillates parallel to the x...
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 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?
2. The amplitude of a damped harmonic oscillator drops to 1/e of its initial value after n complete cycles. Show that the ratio of the period of oscillator to the period of the same oscillator with no damping is given by Td To when n is large.
1. The frequency of a damped harmonic oscillator is 100 Hz, and the ratio of the amplitude of two successive maxima is one half. a. What is the natural (undamped) frequency of this oscillator, in Hertz? b. If the oscillator is launched at time t0 from the origin with speed 2 m/s, what is its speed at time t 0.0140 sec?
7. (a) Explain what is meant by damped harmonic motion, and write down a differential equation describing this phenomenon b) Give an example of a damped harmonic oscillator in practice. Sketch the oscilla- tions it undergoes, and calculate their frequency and damping rate for a natural (undamped) frequency wo 10 Hz and damping coefficient γ-: 2.0 s-1
7. (a) Explain what is meant by damped harmonic motion, and write down a differential equation describing this phenomenon b) Give an example...
58 For the damped oscillator system shown in Fig. 15-16, with m 250 g, k 85 N/m, and b - 70 g/s, what is the ratio of the oscil- lation amplitude at the end of 20 cycles to the initial oscillation amplitude? Rigid support Springiness, k Mass m Vane Damping, b Figure 15-16 An idealized damped simple harmonic oscillator. A vane immersed in a liquid exerts a damping force on the block as the block oscillates parallel to the x...
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...
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