Products
Rewards
from HOLOOLY

We are determined to provide the latest solutions related to all subjects FREE of charge!

Enjoy Limited offers, deals & Discounts by signing up to Holooly Rewards Program

HOLOOLY

HOLOOLY
TABLES

All the data tables that you may search for.

HOLOOLY
ARABIA

For Arabic Users, find a teacher/tutor in your City or country in the Middle East.

HOLOOLY
TEXTBOOKS

Find the Source, Textbook, Solution Manual that you are looking for in 1 click.

HOLOOLY
HELP DESK

Need Help? We got you covered.

## Q. 2.16

Transfer Function—One Equation of Motion

PROBLEM: Find the transfer function, $X(s)/F(s)$, for the system of Figure 2.15(a).

## Verified Solution

Begin the solution by drawing the free-body diagram shown in Figure 2.16(a). Place on the mass all forces felt by the mass. We assume the mass is traveling toward the
right. Thus, only the applied force points to the right; all other forces impede the motion and act to oppose it. Hence, the spring, viscous damper, and the force due to acceleration point to the left.

We now write the differential equation of motion using Newton’s law to sum to zero all of the forces shown on the mass in Figure 2.16(a):

$M\frac{d^{2}x(t) }{dt^{2} } +ƒ_{\nu } \frac{dx(t)}{dt}+Kx(t) =ƒ(t)$

Taking the Laplace transform, assuming zero initial conditions

$Ms^{2} X(s)+ƒ_{\nu }X(s) +KX(s)=F(s)$

or

$(Ms^{2} +ƒ_{\nu }s+K)X(s)=F(s)$

Solving for the transfer function yields

$G(s)=\frac{X(s)}{F(s)} =\frac{1}{Ms^{2}+ƒ_{\nu }s+K }$

which is represented in Figure 2.15(b).