Properties of Damped Oscillations For Problems 1-4, determine the damped amplitude, the damped na...
1. Oscillating system performs damped oscillations with frequency 1000 Hz. Determine the frequency of natural oscillations if the resonance frequency is 998 Hz. 2. Amplitude of vibrations during 5 minutes decreased by 2 times, during which time the amplitude reduced by 8 times? 3. For 8 minutes amplitude decreased 8 times. Find damping factor. 4. Determine how much resonance frequency is different from the natural oscillation frequency (1kHz) when the damping factor is 400 s decreased 20 times 6. The...
In solving for the damped forced circuit 1 oscillations (particular solution) has the form 6. +R q-Vocos(r) + dt C we found the pers istent cos (st where γ -, LC 21 2 Define rso that the amplitude of the response is proportional toT(r)- where we (1-r2)2 +4γ assume γ is a set constant (i) Show that T has a maximum Tmax-T(rmax) if γく1. In such a case find "max and T,nax (ii) Plot in T vs. r for the...
Exercise 3 (15pts) A control system is given by the second order transfer function bellow: Natural frequency of oscillations Damped ratio Determine the range of values of K that render the system underdamped Pick one of those values of K (of your choice) and determine 1. 2. 3. 4. a. Percentage overshoot b. Settling time c. Peak time Exercise 3 (15pts) A control system is given by the second order transfer function bellow: Natural frequency of oscillations Damped ratio Determine...
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...
Problem # 4 15 points The base of a damped spring-mass system, with m 25 kg and k 2500 N/m, is subjected to a harmonic excitation y(t) Xo cos ω. The amplitude of the mass is found to be 0.05 m when the base is excited at the natural frequency of the system with Yo 0.0 m. Determine the damping constant of the system.
8. + 0.5/1 points Previous Answers OSUniPhys1 15.5.WA.046. My Note A vertical spring-mass system undergoes damped oscillations due to air resistance. The spring constant is 2.50 x 10 N/m and the mass at the end of the spring is 15.0 kg. (a) If the damping coefficient is b = 4.50 N. s/m, what is the frequency of the oscillator? 6.498 ✓ Hz (b) Determine the fractional decrease in the amplitude of the oscillation after 7 cycles. 316 x What is...
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 3 (4 points) NEAR-RESONANCE CASE. (1) Determine the frequency and period of the beats, (2) Determine the frequency and period of the rapid oscillations . (3) USE (1) and (2) to give a rough sketch of a typical solution: THE PERIODS of the beats and of the rapid oscillations MUST BE SHOWN on the t-axes. If they are not shown or are different from the computed periods in (1) and (2) NO POINTS will be given for (3) V8...
solve d ,e , f, g ® Consider a damped unforced mass-spring system with m 1, γ 2, and k 26. a) (2 points) Find if this system is critically damped, underdamped, or overdamped. b) (4 points) Find the position u(t) of the mass at any time t if u(0)-6 and (0) 0. c) (4 points) Find the amplitude R and the phase angle δ for this motion and express u(t) in the form: u(t)-Rcos(wt -)e d) (2 points) Sketch...
5. For each of the following, determine if the system is underdamped, undamped, critically damped or overdamped ad sketch the it step response (a) G (s) = (c) G(s)-t 2+68+ (d) G (s) = 36 6. The equation of motion of a rotational mechanical system is given by where θ° and θί are respectively, output and input angular displace- ments. Assuming that all initial conditions are zero, determine (a) the transfer function model. (b) the natural frequency, w natural frequency,...