1. Answer ALL parts (a) - (c) The dynamic pressure in GPa from a gas explosion on the ceiling of a room can be estimated by P(t) = 86test, where is the number of seconds since the explosion. (a) Find when the pressure will reach its peak value. (b) Calculate the value of the maximum pressure.
1. Answer ALL parts (a) - (c) The dynamic pressure in GPa from a gas explosion on the ceiling of a room can be estimated by P(t) = 86test, where is the number of seconds since the explosion. (a) Find when the pressure will reach its peak value. (b) Calculate the value of the maximum pressure.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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part a and b from question 1 please
![1.
Answer ALL parts (a) - (c)
The dynamic pressure in GPa from a gas explosion on the ceiling of a room can be estimated
by P(t) = 86te-025, where is the number of seconds since the explosion.
(a) Find when the pressure will reach its peak value.
(b) Calculate the value of the maximum pressure.
(c) Use Newton's method to calculate when the pressure will fall to the half of the peak value.
Start from a guess time that is greater than the time calculated from (a) and stop after you
have completed 2 rounds of iteration.
2.
(d) Sketch the pressure curve as the function of time and use the curve to explain what
would happen if the chosen guess time were smaller than the time calculated from (a).
Answer ALL parts (a) - (c)
A one degree of freedom damped mass-spring system is subjected to an impulse
load. The dynamic equilibrium equation of the system is below
dªx(1)
dt²
+2dx(t)
dt
²+x(t) = u(t)- u(t− 3)
Where x(t) is the displacement of the mass at time t, u(t) and u(t-3) are two step
(Heaviside) functions of time.
(A.1)
(a) Draw a graph of the impulse force u(t)-u(t-3) and state what is the duration of
the impulse.
(b) Assume the initial displacement and initial velocity are all zero,
(1) Find the Laplace Transfer of the displacement of the system (show workings)
(2) Find the displacement as a function of time using inverse Laplace transform
(show workings) (hint: L[x(t− a)u(t− a)] = e-sax(s) may be used in the
inverse Laplace Transform)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F98a2975c-b075-4e7f-95a3-3742d529c071%2F105f5416-ba1c-4aa0-b3bd-c91aa7af4edd%2Fm4mjsz_processed.png&w=3840&q=75)
Transcribed Image Text:1.
Answer ALL parts (a) - (c)
The dynamic pressure in GPa from a gas explosion on the ceiling of a room can be estimated
by P(t) = 86te-025, where is the number of seconds since the explosion.
(a) Find when the pressure will reach its peak value.
(b) Calculate the value of the maximum pressure.
(c) Use Newton's method to calculate when the pressure will fall to the half of the peak value.
Start from a guess time that is greater than the time calculated from (a) and stop after you
have completed 2 rounds of iteration.
2.
(d) Sketch the pressure curve as the function of time and use the curve to explain what
would happen if the chosen guess time were smaller than the time calculated from (a).
Answer ALL parts (a) - (c)
A one degree of freedom damped mass-spring system is subjected to an impulse
load. The dynamic equilibrium equation of the system is below
dªx(1)
dt²
+2dx(t)
dt
²+x(t) = u(t)- u(t− 3)
Where x(t) is the displacement of the mass at time t, u(t) and u(t-3) are two step
(Heaviside) functions of time.
(A.1)
(a) Draw a graph of the impulse force u(t)-u(t-3) and state what is the duration of
the impulse.
(b) Assume the initial displacement and initial velocity are all zero,
(1) Find the Laplace Transfer of the displacement of the system (show workings)
(2) Find the displacement as a function of time using inverse Laplace transform
(show workings) (hint: L[x(t− a)u(t− a)] = e-sax(s) may be used in the
inverse Laplace Transform)
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