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Chapter 4: Q2 E (page 227)

In the following problems, take g=32ft/sec2for the U.S. Customary Systemg=9.8m/sec2 and for the MKS system.

Sketch the frequency response curve (13) for the system in which m = 2, k = 3, b = 3.

Short Answer

Expert verified

Therefore, the frequency response curve is M纬=13-2纬22+9纬2. and its sketch is shown below.

Step by step solution

01

General form

The angular frequency:

The amplitude of the steady-state solution to equation (1) depends on the angular frequency of the forcing function and it is given by A纬=F0M纬, where

M纬:=1k-m纬22+b2纬2鈥�鈥�鈥�鈥�鈥�鈥�鈥�鈥�鈥�鈥�鈥�鈥�鈥�鈥�鈥�鈥�鈥�鈥�1

02

Evaluate the equation

Given that the frequency response curve isM纬=1k-m纬22+b2纬2.

And m = 2, k = 3, and b = 3.

Substitute the values in equation (1).

M纬=13-2纬22+9纬2

Now draw the graph for it.

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Most popular questions from this chapter

Vibrating Spring without Damping. A vibrating spring without damping can be modeled by the initial value problem(11)in Example3 by taking b=0.

a) If m=10kg,k=250kg/sec2,y(0)=0.3m, and y'(0)=-0.1m/sec, find the equation of motion for this undamped vibrating spring.

b)After how many seconds will the mass in part (a) first cross the equilibrium point?

c)When the equation of motion is of the form displayed in (9), the motion is said to be oscillatory with frequency 尾/2蟺. Find the frequency of oscillation for the spring system of part (a).

Find a general solution y''+4y'+8y=0

Vibrating Spring with Damping. Using the model for a vibrating spring with damping discussed in Example3

(a)Find the equation of motion for the vibrating spring with damping ifm=10kg,b=60kg/sec,k=250kg/sec2,y(0)=0.3m,andy'(0)=-0.1m/sec.

(b)After how many seconds will the mass in part(a) first cross the equilibrium point?

(c)Find the frequency of oscillation for the spring system of part (a).

(d)Compare the results of problems32 and33determine what effect the damping has on the frequency of oscillation. What other effects does it have on the solution?

In Problems 35, use the method of undetermined coefficients to find a particular solution to the given higher-order equation.y'''+y''-2y=tet

The auxiliary equations for the following differential equations have repeated complex roots. Adapt the "repeated root" procedure of Section 4.2 to find their general solutions:

(a)y''''+2y''+y=0

(b)y''''+4y'''+12y''+16y'+16y=0
See all solutions

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