Equilibrium of Force System

The body is said to be in equilibrium if the resultant of all forces acting on it is zero. There are two major types of static equilibrium, namely, translational equilibrium and rotational equilibrium.
 

Formulas
Concurrent force system
ΣFx=0

ΣFy=0
 

Parallel Force System
ΣF=0

ΣMO=0
 

Non-Concurrent Non-Parallel Force System
ΣFx=0

ΣFy=0

ΣMO=0
 

Problem 03 | Laplace Transform by Integration

Problem 03
Find the Laplace transform of   f(t)=sinbt.
 

Problem 03
L{f(t)}=0estf(t)dt

L(sinbt)=0estsinbtdt
 

For   0estsinbtdt.

Using integration by parts:   udv=uvvdu.   Let

Problem 02 | Laplace Transform by Integration

Problem 02
Find the Laplace transform of   f(t)=eat.
 

Solution 02
L{f(t)}=0estf(t)dt

L(eat)=0esteatdt

L(eat)=0est+atdt

L(eat)=0e(sa)tdt

L(eat)=1sa0e(sa)t[(sa)dt]

Problem 01 | Laplace Transform by Integration

Problem 01
Find the Laplace transform of   f(t)=1   when   t>0.
 

Solution 01
L{f(t)}=0estf(t)dt

L(1)=0est(1)dt

L(1)=0estdt

L(1)=1s0est(sdt)

L(1)=1s[est]0

Laplace Transform

Definition of Laplace Transform

Let   f(t)   be a given function which is defined for   t0. If there exists a function   F(s)  so that
 

F(s)=0estf(t)dt,

 

then   F(s)   is called the Laplace Transform of   f(t), and will be denoted by   L{f(t)}.   Notice the integrator   estdt   where   s   is a parameter which may be real or complex.
 

Engineering Economy

Simple Interest, Compounded Interest, Annuity, Capitalized Cost, Annual Cost, Depreciation, Depletion, Capital Recovery, Property Valuation or Appraisal, Principles of Accounting, Cost Accounting, Break-even Analysis, Minimum Cost Analysis, Public Economy, Inflation and Deflation, Risk and Uncertainty.

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