Homework Answers
In this problem, the ratio of the time period of oscillator to
the time period of the same oscillator with no damping is given by
as shown below procedure.
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2. The amplitude of a damped harmonic oscillator drops to 1/e of its initial value after...
Q.3 Consider a damped harmonic oscillator. After four cycles the amplitude of the oscillator has dropped...
Q.3 Consider a damped harmonic oscillator. After four cycles the amplitude of the oscillator has dropped to 1/e of its initial value. Find the ratio of the frequency of the damped oscillator to its natural frequency.
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?
Problem 3 A damped harmonic oscillator is described by the displacement as a function of time,...
Problem 3 A damped harmonic oscillator is described by the displacement as a function of time, An observer finds that every time the mass reaches its maximum (positive) displacement, that displacement is 10.0% smaller than the previous maximum positive displacement. Calculate the ratio of the period T of the oscillator with damping, to the period To of the same oscillator without damping.
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...
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?
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?
1. An ideal (frictionless) simple harmonic oscillator is set into motion by releasing it from rest...
1. An ideal (frictionless) simple harmonic oscillator is set into motion by releasing it from rest at X +0.750 m. The oscillator is set into motion once again from x=+0.750 m, except the oscillator now experiences a retarding force that is linear with respect to velocity. As a result, the oscillator does not return to its original starting position, but instead reaches = +0.700 m after one period. a. During the first full oscillation of motion, determine the fraction of...
For lightly damped harmonic oscillators the displacement is given by x(t) = (A^(-bt/2m))*cos(ωt + φ) with period T = 2π...
For lightly damped harmonic oscillators the displacement is given by x(t) = (A^(-bt/2m))*cos(ωt + φ) with period T = 2π / (sqrt((k/m)-(b^2/(4m^2)))). A) Show that this equation of motion obeys the force equation for a damped oscillator: F = −kx − bv. B) Shock absorbers in a pickup truck are designed to have a significant amount of damping. The effective spring constant of the four shock absorbers in a 1600 kg truck have an effective spring constant of 157,000 N/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.
2. A damped harmonic oscillator with m 1.00 kg, k 2500 N/m, and b 42.4 kg/s...
2. A damped harmonic oscillator with m 1.00 kg, k 2500 N/m, and b 42.4 kg/s is subject to a driving force given by Fo cos wt. (a) what value of ω results in the maximum stead-state amplitude (ie, resonance)? (b) What is the quality factor Q of this oscillator?
Q.3 Consider a damped harmonic oscillator. After four cycles the amplitude of the oscillator has dropped to 1/e of its initial value. Find the ratio of the frequency of the damped oscillator to its natural frequency.
Problem 3 A damped harmonic oscillator is described by the displacement as a function of time, An observer finds that every time the mass reaches its maximum (positive) displacement, that displacement is 10.0% smaller than the previous maximum positive displacement. Calculate the ratio of the period T of the oscillator with damping, to the period To of the same oscillator without damping.
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...
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?
1. An ideal (frictionless) simple harmonic oscillator is set into motion by releasing it from rest at X +0.750 m. The oscillator is set into motion once again from x=+0.750 m, except the oscillator now experiences a retarding force that is linear with respect to velocity. As a result, the oscillator does not return to its original starting position, but instead reaches = +0.700 m after one period. a. During the first full oscillation of motion, determine the fraction of...
2. A damped harmonic oscillator with m 1.00 kg, k 2500 N/m, and b 42.4 kg/s is subject to a driving force given by Fo cos wt. (a) what value of ω results in the maximum stead-state amplitude (ie, resonance)? (b) What is the quality factor Q of this oscillator?
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