Concept explainers
The relation between the tension T and the steady shortening velocity v in a muscle is given by the Hill equation:
(T+a)(v+b) = (T0+a)b
where a and b are positive constants and T0is the isometric tension. i.e., the tension in the muscle when v = 0. The maximum shortening velocity occurs when T = 0.
(a) Using symbolic operations, create the Hill equation as a symbolic expression. Then use subs to substitute T = 0, and finally solve for v to show that vmax=bT0)/a. (b) Use vmax from part (a) to eliminate the constant b from the Hill equation, and show that
Want to see the full answer?
Check out a sample textbook solutionChapter 11 Solutions
EBK MATLAB: AN INTRODUCTION WITH APPLIC
- What are static error coefficients? how will you calculate the steady state error using static error coefficients? (Write equations also, about kp, Kv, Ka) subject: control systemarrow_forwardQ2 For the system shown in the figure below 1. Calculate the static velocity error Kv, 2. Determine the poles and zeros of this system. 3. The values of K that will result in zero overshoot for unit step input. 4. Write an expression for the overshoot for a step input. R(s) 100 C(s) s2 Ksarrow_forwardQ2) A system is shown in the figure below Given that x=20 and y =30 Determine a) The steady State error for a unit step input in terms of D and F where E(s)=Z:(s)-Z2(s) b) Select a value for D so that the steady state error is zero F D (s +x)(s+y)arrow_forward
- The damping ratio of the system is zero and nature of the out put is pure exponential. Select one: True False Previous page Next pagearrow_forward2. Find the static error constants and the steady-state error for the digital system shown in Figure P2 if the inputs are a. u(t) b. tu(t) C. t²u(t) R(z) - 0.13(z + 1) (z-1)(z-0.74) C(z) Figure P2arrow_forward31 A first-order system has a time constant of 30 s. What will be its delay time and rise time when subject to a unit step input? 32 A first-order system when subject to a unit step input rises to 90% of its steady-state value in 20 s. Determine its time constant, delay time and rise time? 33 Determine the natural angular frequency, the damping factor, the rise time, percentage overshoot and 2% settling time for systems with the following transfer functions: (a) 100/(s + 4s + 100), (b) 49/(s + 4s + 49). 34 Determine the natural angular frequency, the damping factor, the rise time, percentage overshoot and 2% settling time for a system where the output y is related to the input x by the differential equation: 쫓+5%+16y= 16x s(s + dz2 dr 35 For the feedback system shown in Figure 10.16, what gain K should be used to give a rise time of 2 s? Figure 10.16 Problem 35arrow_forward
- Task 2: Consider the electrical system in the figure below, derive a differential equation that expresses the relation between the rate of change in the capacitor voltage Vc, and the voltage across the resistor VR. (Hint: use Kirchhoff current law). (i) (ii) (iii) СЕ Formulate a first order differential equation to express the previous system. Hint: use Kirchhoff current law. Find the general solution of this first order differential equation, Assume: C-50 Micro Farad and R=50 ohm. Show how this differential equation could also be solved using Laplace transform to determine the particular solution. Table of Laplace transforms A to 4 T 12 sin kr cask! k 446 Fis) = Lif(t)) (+4)² a 320 15-A $5-A R 12.0 y>0 ²+²>0 L{f'(r)] = $F(s)-f(0) Lif"(t)) = s²F(s) - sf (0) - f'(0)arrow_forwardYou are given five light bulbs designed to operate on 160 mA current at 3.0 V (rms values), arid want to connect them in parallel, through an ideal transformer, to 120 V rms AC household power. a) Draw a circuit diagram showing the AC power source (a generator symbol ), the transformer, and resistors for the light bulbs. b) Is the required transformer step-up or step-down? What turns ratio N5/N is needed? e) Calculate the ruts current through both the primary and secondary coils of the trans former, in mA.arrow_forwardThe damping ratio and peak overshoot are measures of: Speed of response Steady state error O Relative stability O Absolute stabilityarrow_forward
- Power System Analysis and Design (MindTap Course ...Electrical EngineeringISBN:9781305632134Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. SarmaPublisher:Cengage Learning