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 harmonic oscillator with mass m , natural angular frequency ω0 , and damping constant r...
3.4. A harmonic oscillator with mass m, natural angular frequency wo, and damping constant r is driven by an external force FCt) Fo cos(wot)N. W show that xp A sin(wot) is a solution if A Fo/rwo. rite the equation of motion and use it to
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.
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. A spring-mass system has mass m, spring constant k, and hence natural frequency ω0 = (k/m)^1/2 . The damping constant can take any value. Show that the smallest half-life you can get without the spring becoming overdamped is (ln2 / ω0) .
3. Power in a DHO. The power developed in a mechanical system is force x velocity. Show that the average power dissipated by the damping in a DHO is: (b) Evaluate this expression at o r, the resonant frequency from Problem 2. Show that the average driving power, <Pin is: (Hint: The average of cos2@t-ф) is %.) Useful Formulae Natural Frequency co-sqrt(km); ω0-2to; simple harmonic oscillator: d2x/dt2 + 002x-0; Forced Damped Harmonic Oscillator (DHO): m"(d2x/dt2) + b*(ds/dt) + kx =...
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.
[4] Consider a harmonic oscillator of mass m and angular frequency ω. At time t-0, the state of this oscillator is given by y(о) со фо) + с ф.) where the states I 0) .) represent the ground state and first excited state respectively. (a) Write the normalization condition for lv(o) and determine the mean value (H) of the energy in terms of co and ci. (b) With the additional requirement (H)-ho. calculate eoand o,p. [4] Consider a harmonic oscillator...
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 particle undergoes damped harmonic motion. The spring constant is 100 N/m; the damping constant is 8.0 x 10-3 kg∙m/s, and the mass is 0.050 kg. If the particle starts at its maximum displacement, x = 1.5 m, at time t = 0, what is the angular frequency of the oscillations?
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...