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 (b) (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. If the function of Force at particular time is given as F(t) = Fo sin wžt. Determine the particular solution. (iii)
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 (b) (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. If the function of Force at particular time is given as F(t) = Fo sin wžt. Determine the particular solution. (iii)
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Transcribed Image Text:Figure Q1(b): Mass spring damping system
F(t)2

Transcribed Image Text:(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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