An experiment was carried out on a SDOF system to estimate the natural frequency and damping. The time history plotted below has the response in centimetres and the time in seconds, as shown in Figure Q10 below. Estimate values for the following and choose the nearest values from the list given below: the damped natural frequency in Hz; the damping ratio using the logarithmic decrement method; and the natural frequency in rad/s. Ju(t) 2.00 1.00 0.00 0.00 MA Figure Q10 T 0.80 1.60 Select one or more: O a. 4.92 b. 0.781 D c. 0.625 Od. 0.330 Oe. 0.052 2.40 I 3.20 4.00 t

1 Problem You are given the following data (below) showing the steady-state output response, x(t), of a mass-spring-damper (stable, LTI) system to a sinusoidal input u(t) = A sin(wt). This snapshot is the response after all the transients have decayed (the time is shifted to start at zero for conve- nience). x 0.5225 Displacement pu(t) Sinusoidal force input x 0.1041 1.5 1 Y2 х 0.2783 Y1.372 0.5 h ok -0.5- -1 -1.5 x(t) M Assume: bl u(t) x(t) Horizontal Plane (no gravity) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Time (sec) www k Using only the data provided above (the blue line is the input u(t) and the red line is the output x(t)), determine: 1. The frequency of the input in rad/s 2. The amplitude of the input, A 3. The frequency of the output in rad/s 4. The output-input ratio |G(iw)| = max(x(t)) max(u(t))' at the particular input frequency shown. 5. The phase (also called phase lag) of the output, $, at the particular input frequency shown in degrees. Note the phase is generally…

A test was undertaken to find the dynamic properties of a SDOF system. The measured transient response recorded is shown in Figure QA2a. If the stiffness of the system is 1,000 N/m estimate: i) the damping ratio, ii) the undamped natural frequency, and iii) the mass of the system. Displacement (m) 0.08 0.06 0.04 0.02 O -0.02 -0.04 -0.06 -0.08 Figure QA2a 0.5 Time (s) 1.5 2

Matlab

otoring: MITO R (Motor) = VAPPL Torque [N*m] 60 T 0₁ V 200 rad/s W₁ Viscous Friction b₁ N₁ J₁ 2 N₂ b₂ Viscous Friction J₂ VMOTOR K, W₁ T=K₁ i 0₂ ta from the steady state dynamometer test and the given values: J₁ ², b₁ 2N, b2 = 12N, N₁ = 50 teeth, N₂ = 100 teeth (R should rad'

Sketch frequency response of the system from part (a) in the form of Bode plot as accurately as you can.

(c) An electronic Pl temperature controller has an output p of 15 mA when the set point equals the nominal process temperature. The controller response to step change in the temperature set point of 3 mA is shown below. t(s) 0- 0+ 20 60 80 Determine the controller gain K, and the integral time.r p (mA) 8,0 6,8 6.0 4.4 3.6

4) Consider the system below. Write the equation of motion and calculate the response assuming that the system is initially at rest for the values k₁ 100[N/m], k2= 100[N/m], k3 = 200[N/m], 100[N/m], k5 = 50[N/m], k6: 50[N/m], and m = = [10kg]. Solve the equation of motion k4 = as a differential equation = F(t) = 80 cos (20t) K5 Κι www K3 ΚΑ m www K6 K2

I need help with this please.

A) Assuming that no inputs are present to a first-order and a second-order systems, mention two fundamental differences between the two systems. B) Determine the damping ratio and natural frequency of the single-loop RLC electrical circuit system shown below. d²1 dI I + R + = dt² dt с L E(t). C) State two distinctions between odd and even functions, and name and sketch a function that's neither odd nor even. D) What is the frequency in Hertz and the amplitude of the 5th term (i.e. the 4th harmonics) of the following signal? 4 2π 10π == - sin TT 4 бп y(t) (² t) + 37 sin (17) 4 + sin 5π (10+) +. 10 10