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3.4. A harmonic oscillator with mass m, natural angular frequency wo, and damping constant r is...
A harmonic oscillator with mass m , natural angular frequency ω0 , and damping constant r...
A harmonic oscillator with mass m , natural angular frequency ω0 , and damping constant r is driven by an external force F(t) = F0cos(ωt). Show that if ω = ω0, then the instantaneous power supplied by the driving force is exactly absorbed by the damping force.
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,...
3. When an oscillator with natural frequency wo is driven by another oscillator with a different ...
3. When an oscillator with natural frequency wo is driven by another oscillator with a different natural frequency w, the phenomenon of beats can occur. The existence of beats is very useful when tuning a string instrument by ear. Show that the solution of the undamped oscillator IVP y', +Hy-Asin(wt), y(0)--, wo+w with y(0)-0, leads to beats, by first solving the IVP and then plotting the solution using MATLAB for A w = 1.1 and t є [0, 1001. 1,...
13. A damped mass-spring system with mass m, spring constant k, and damping constant b is...
13. A damped mass-spring system with mass m, spring constant k, and damping constant b is driven by an external force with frequency w and amplitude Fo. 2662 where, wo is the (a) Show that the maximum oscillation amplitude occurs when w = natural frequency of the system. where, wd is the (b) Show that the maximum oscillation amplitude at that frequency is A = frequency of the undriven, damped system.
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 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.
help with 1-3 1) A simple harmonic oscillator consists of a 0.100 kg mass attached to...
help with 1-3
1) A simple harmonic oscillator consists of a 0.100 kg mass attached to a spring whose force constant is 10.0 N/m. The mass is displaced 3.00 cm and released from rest. Calculate (a) the natural frequency fo and period T (b) the total energy , and (c) the maximum speed 2) Allow the motion in problem 1 to take place in a resisting medium. After oscillating for 10 seconds, the maximum amplitude decreases to half the initial...
1.- Starting from the differential equation for a 1-degree of freedom system with mass M, damping...
1.- Starting from the differential equation for a 1-degree of freedom system with mass M, damping c and spring stiffness k: a.- Show that the particular solution for the equation with an applied force fo cos(ot), i.e., Mä+ci+kx=f, cos(or) can be expressed as x )= A cos(ot) + A, sin(or) and find the values of A, and A, that solve the differential equation in terms of M, c, k and fo. 5 points. b. Use the result from part a...
A forced oscillator is driven at a frequency of 30 Hz with a peak force of...
A forced oscillator is driven at a frequency of 30 Hz with a peak force of 17 N. The natural frequency of the physical system is 26 Hz. If the damping constant is 1.25 kg/s and the mass of the oscillating object is 0.75 kg, calculate the amplitude of the motion 3.842473x mm
The equation of motion of a harmonic oscillator of mass m is ? ? = ?...
The equation of motion of a harmonic oscillator of mass m is ? ? = ? ∙ ??? ?? . By analogy with the Bohr atom, define angular momentum, ? = ?v?, and quantize its maximum value ! according to ?!"# = ?ħ. The relationship between k, m, and ω is: ? = ?? . (a) Show that the total mechanical energy of the oscillator is quantized according to ? = ?h?, where ? is the frequency of oscillation. (b)...
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,...
3. When an oscillator with natural frequency wo is driven by another oscillator with a different natural frequency w, the phenomenon of beats can occur. The existence of beats is very useful when tuning a string instrument by ear. Show that the solution of the undamped oscillator IVP y', +Hy-Asin(wt), y(0)--, wo+w with y(0)-0, leads to beats, by first solving the IVP and then plotting the solution using MATLAB for A w = 1.1 and t є [0, 1001. 1,...
13. A damped mass-spring system with mass m, spring constant k, and damping constant b is driven by an external force with frequency w and amplitude Fo. 2662 where, wo is the (a) Show that the maximum oscillation amplitude occurs when w = natural frequency of the system. where, wd is the (b) Show that the maximum oscillation amplitude at that frequency is A = frequency of the undriven, damped system.
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).
help with 1-3
1) A simple harmonic oscillator consists of a 0.100 kg mass attached to a spring whose force constant is 10.0 N/m. The mass is displaced 3.00 cm and released from rest. Calculate (a) the natural frequency fo and period T (b) the total energy , and (c) the maximum speed 2) Allow the motion in problem 1 to take place in a resisting medium. After oscillating for 10 seconds, the maximum amplitude decreases to half the initial...
1.- Starting from the differential equation for a 1-degree of freedom system with mass M, damping c and spring stiffness k: a.- Show that the particular solution for the equation with an applied force fo cos(ot), i.e., Mä+ci+kx=f, cos(or) can be expressed as x )= A cos(ot) + A, sin(or) and find the values of A, and A, that solve the differential equation in terms of M, c, k and fo. 5 points. b. Use the result from part a...
A forced oscillator is driven at a frequency of 30 Hz with a peak force of 17 N. The natural frequency of the physical system is 26 Hz. If the damping constant is 1.25 kg/s and the mass of the oscillating object is 0.75 kg, calculate the amplitude of the motion 3.842473x mm
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