SYSTEM DYNAMICS CONNECT
3rd Edition
ISBN: 9781264201730
Author: Palm
Publisher: MCG CUSTOM
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Chapter 5, Problem 5.15P
Obtain the state model for the two-mass system whose equations of motion are
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A mass, m, is hung from an ideal spring (its length is equal to zero and no friction) and reaches equilibrium at position B when the spring has been stretched to the length l. The mass is then pulled to position C and released. The position C is of height h below the position B. The mass oscillates between positions A and C. [Neglect friction.] At which position, A, B, or C, is mass m located when the kinetic energy, gravitational potential energy, or elastic potential energy of the system is at a maximum? Explain the reason for each case.
1 ) Derive a free body diagram with spring-mass-damper elements for given system. QUESTION 2 ) Derive equation of motion for given system in terms of m, c, k.
The equivalent spring stiffness of an inclined spring whose k = 5 N/m and angle of inclination θ = 35°
3.355 N/m
4.095 N/m
5.867 N/m
4.511 N/m
Chapter 5 Solutions
SYSTEM DYNAMICS CONNECT
Ch. 5 - Prob. 5.1PCh. 5 - Obtain the transfer function Xs/Fs from the block...Ch. 5 - Obtain the transfer function Xs/Fs from the block...Ch. 5 - Draw a block diagram for the following equation....Ch. 5 - Draw a block diagram for the following model. The...Ch. 5 - Referring to Figure P5.6, derive the expressions...Ch. 5 - Prob. 5.7PCh. 5 - Prob. 5.10PCh. 5 - Obtain the state model for the reduced-form model...Ch. 5 - Obtain the state model for the reduced-form model...
Ch. 5 - Prob. 5.13PCh. 5 - Obtain the state model for the transfer-function...Ch. 5 - Obtain the state model for the two-mass system...Ch. 5 - Prob. 5.16PCh. 5 - Put the following model in standard state-variable...Ch. 5 - Given the state-variable model...Ch. 5 - Given the following state-variable models, obtain...Ch. 5 - Prob. 5.20PCh. 5 - The transfer function of a certain system is...Ch. 5 - Prob. 5.22PCh. 5 - Prob. 5.23PCh. 5 - Use MATLAB to obtain a state model for the...Ch. 5 - Use MATLAB to obtain a state-variable model for...
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- The equation of motion of a certain mass-spring-damper system is 5x'' + cx' +10x = f(t). Suppose that f(t) = Fsin(wt). Define the magnitude ratio as M = X/F. Determine the natural frequency w_n, the peak frequency w_p, and the peak magnitude ratio M_p for damping ratio = 0.1 and the damping ratio = 0.3arrow_forwardThe mechanical system shown in Figure 1 is initially at rest. The displacement x of mass m is measured from the rest position. With m = 10 kg, b = 20 N-s/m, and k = 500 N/m, the system is set into motion at t=0 by an impulsive force whose strength is 20 N. Obtain the initial velocity *(0,) of the mass due to the impulsive force.arrow_forwardIn the figure, a disk-shaped wheel of mass M and radius R rolls without slipping on a circular platform of radius 2L+R. The wheel is attached by a torsion spring to a pendulum of length 2L of mass m and moves with this pendulum.a) Derive the differential equation for the motion of the system given here.b) Find the natural frequency of the free motion of the system. L=2 [m], R= 0,5 [m], m=5 [kg], M= 65[kg], kb= 165 [Nm/rad] Note: There is no friction in this systemarrow_forward
- For the rotational mechanical system shown, find the transfer function Ɵ1(s)/T(s) and Ɵ2(s)/T(s).arrow_forwardA mass weighing 40 N stretches a spring 0.1 m. The spring–the mass system resides in a medium with a damping constant of 32N-s m. If the mass is released from its equilibrium position witha velocity of 0.1 m/ s in the downward direction, find the time required for the mass to return to its equilibrium position for thefirst timearrow_forwardObtain the state matrices for the system considering as output:C). Velocity m3 with respect to m2.arrow_forward
- Suppose a spring with spring constant k=1 supports a mass of 1kg and is subject to a driving force f(t)=sin2t. The mass is initially at rest at its equilibrium point. At time t=2, the mass is hit with a sharp upward blow, so that the force of the blow is δ(t−2). Set up and solve (using Laplace transforms) an initial-value problem modelling this situation.arrow_forwardSubject: Dynamics of Rigid Bodiesarrow_forward(c) The spring-damper-mass system shown in Figure Q3(c) is at rest when strict by a hammer with an initial velocity of 0.4 m/s causing the mass to move upwards. Given that the mass m = 2 kg, spring constant k = 128 N/m and coefficient of viscous damping c = 0.6 Ns/m. (i) Determine the damped frequency of the spring-damper-mass system.arrow_forward
- 1) Obtain a state space model of the system. 2) Given m =1 kg, k = 1 N/m and b = 1 N.s/m is the system Controllable? 3) For what values of k,m,b the system is stable? Explain your answer?arrow_forwardquestion 2 A mass ! hangs on the end of a cord around a pulley of radius 5 and moment of inertia 6, rotating with an angular velocity ,, as shown in the figure below. The rim of the pulley is attached to a spring (with constant 7). Assume small oscillations so that the spring remains essentially horizontal and neglect friction so that the conservation of energy of the system yields: 1 2 !91 + 1 2 6,1 + 1 2 7;1 − !); = =, ?ℎABA , = 9 5 , = = CDE&/, ; = FG&H'5CA!AE/ IBD! AJ(G'GKBG(! Find the natural circular frequency of the system in terms of !, 5, 7,6, and ).arrow_forwardThe block diagram shown is representing the dynamic system. Obtain the transfer function C(s)/R(s)by the method of reduction of blocks.arrow_forward
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