Answer: ε₁+ε₂+ε₃ = 0
Explanation: Considering the initial and final volume to be constant which gives rise to the relation:-
l₀l₀l₀=l₁l₂l₃
taking natural log on both sides
Considering the logarithmic Laws of division and multiplication :
ln(AB) = ln(A)+ln(B)
ln(A/B) = ln(A)-ln(B)
Use the image attached to see the definition of true strain defined as
ln(l1/1o)= ε₁
which then proves that ε₁+ε₂+ε₃ = 0
Answer:
a) Under damped
Explanation:
Given that system is critically damped .And we have to find out the condition when gain is increased.
As we know that damping ratio given as follows
Where C is the damping coefficient and Cc is the critical damping coefficient.
So from above we can say that
From above relationship we can say when gain (K) is increases then system will become under damped system.
Answer:
b) False
Explanation:
in trapezoidal rule the error is proportional to and the order of accuracy is proportional to
.
Trapezoidal rule is numerical integration method .Trapezoidal rule is used to find the area of curves.In trapezoidal rule we finds the approximate value of integration.But the real value of integration will not differ to much from the value which finds by using trapezoidal rule.
Answer:
Explanation:
a) the steady-state, 1-D incompressible and no energy generation equation can be expressed as follows:
b) For a transient, 1-D, constant with energy generation
suppose T = f(x)
Then; the equation can be expressed as:
where;
= heat generated per unit volume
= Thermal diffusivity
c) The heat equation for a cylinder steady-state with 2-D constant and no compressible energy generation is:
where;
The radial directional term = and the axial directional term is
d) The heat equation for a wire going through a furnace is:
since;
the steady-state is zero, Then:
'
e) The heat equation for a sphere that is transient, 1-D, and incompressible with energy generation is: