System Dynamics Homework Help

Consider the following IVP: with initial condition x(to) = -10 and to = 0. x*+2x=0 1. What is the particular solution, x(t)? 2. What is the value of x as time t → ∞? A. x → →∞0 B. x → -10 C. x→0 D. x → +10 E. x → +∞

(ii) Explain the steady-state response of system, Xss(t) to the square-wave input F(t) in this work.

Shaft S turns in a clevis F attached to the ground at 2 rad/sec with respect to the ground indirection shown. The wheel simultaneously rotates about the axis indicated at 3 rad/sec with respect to the shaft S. Both rotation rates are constant. There is a bug crawling outward on a spoke as shown. The bug is currently 1 in. away from the center of the wheel. The bug is crawling outward on the spoke at 0.2 in./sec with an acceleration of 0.1 in./sec?, both relative to the spoke.At the instant shown, find 1. the absolute velocity of the bug with respect to the ground (6 points) 2. the absolute acceleration of the bug with respect to the ground.(9 points) Express your answer in the coordinate system shown attached to the shaft S.

1. A system has a transfer function G(s) given by: G(s)=\frac{5}{(2 s+3)(s+4)} Showing all your working, determine the response of the system in the time domain to a step input at time t = 0 of magnitude 1. Hence state whether the system is stable or unstable.

Problem 2. (1) (2.5 points) DErive the Equations of motion of a quarter-car model shown below. (2) (2.5 points) Obtain the state-space model. (3) (2.5 points) Obtain the transfer function: G(s) = Y(s)/R(s).

Figure P10.3 shows a general closed-loop control system. The plant transfer function is G_{p}(s)=\frac{1}{s^{2}+6 s+8} a. Determine whether the closed-loop system is stable for control gain K, 2. b. Compute the controller gain Kp so that step response shows 25% overshoot. c. Estimate the settling time for a step reference input if the control gain is K, 0.5.

Is it possible to answer question 2d without calculating the inverse Laplace transform? Explain.

2 Frequency Divider Put the 1 uF capacitor back in the circuit. Record the frequency of the 555 output signal for the following trigger frequencies. Question 3 Explain why the 555 ignores some of the trigger pulses at the higher trigger frequencies? (Refer to the 555 diagram for this explanation.)

Given the following system equation 4 z+20 z+84 z=0.12 u a. Obtain a complete SSR with input u and output y 2. b. Derive the system transfer function G(s) = Z(s)/U(s) Derive the transfer function Y(s)/U(s) where the output is y = ż.C.

A coil spring with plain ends that are ground is to operate with a load that fluctuates between 45 and90 lb, đuring which the deflection is to vary by in.Because of space limitations, a mea coil diameterof2 in. has been selected. Steel spring wire corresponding to the shot-peened wire in Figure 12.16 is to be used. The beneficial effect of the specified presettingİs not to be taken into account in the calculations.It is considered to provide a sufficient safety factor to allow for the possibility of higher stresses, should the spring ever close solid. Choose an appropriate clash allowance, and determine appropriate values for N.d. andL (See Figure P12.39.