QI (a) Evaluate equation y" - 3y' - 4y = e* using the Laplace transform, with initial conditions y(0) = -5 and y’(0) = -1. (b) Figure Q1(b) shows a mass of 5kg, in a water tank, is connected with a spring. The mass is pulled down as far as x with an initial Force of Fo = 4N. The spring coefficient and the damping coefficient are known, k = 10N/m and b = 15kg/s, respectively (i) Derive the empirical equation of the homogeneous solution (ii) Compute the homogeneous solution if initial conditions are given, y(0) = 1 and y'(0) = -7. (iii) If the function of Force at particular time is given as F(t) = F, sin wžt. Determine the particular solution. (iv) Evaluate the General equation of non-homogeneous solution. Note that F = m a, and wo =
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![Q1
(a)
Evaluate equation y" – 3y' – 4y = e* using the Laplace transform, with
%3D
initial conditions y(0) = -5 and y`(0) = -1.
(b) Figure Q1(b) shows a mass of 5kg, in a water tank, is connected with a
spring. The mass is pulled down as far as x with an initial Force of Fo :
4N. The spring coefficient and the damping coefficient are known, k =
10N/m and b = 15kg/s, respectively
(i)
Derive the empirical equation of the homogeneous solution
Compute the homogeneous solution if initial conditions are given,
y(0) = 1 and y'(0) = -7.
(ii)
(iii)
If the function of Force at particular time is given as F(t) =
Fo sin wžt. Determine the particular solution.
(iv)
Evaluate the General equation of non-homogeneous solution.
Note that F = m a, and wo =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb74757fc-06fd-4a0a-94e0-364275c5b6b5%2Fa5b5dfc7-c7ef-482c-86d3-b782b0a5928a%2Fi63u7ds_processed.jpeg&w=3840&q=75)
![Figure Q1(b): Mass spring damping system
m2
F(t)2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb74757fc-06fd-4a0a-94e0-364275c5b6b5%2Fa5b5dfc7-c7ef-482c-86d3-b782b0a5928a%2Fjhuc8dx_processed.jpeg&w=3840&q=75)
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