a) A mass, m = 20ON is attached to the free end of a vertical spring as shown Figure Q3(a), where the damping coefficient, c 10N.s/m and the spring constan k = 20N/m. When displaced from the equilibrium position, the mass is subjected to fre vibration response which can be described by the pendulum motion: d2x dx m + c + kx = 0 dt2 dt where x is the horizontal displacement from the equilibrium position and t is time. Th displacement (x) as a function of time t is given below, where the initial velocity y(t=0) zero. - x(t) t (s) x (m) 0.005 0.005 0.005 -0.0575 -0.08875 10 15 20 Figure Q3(a) i) Assume y = , reduce the system to first order differential equation. ii) Determine the first order differential equation over the time period of Osts 20
a) A mass, m = 20ON is attached to the free end of a vertical spring as shown Figure Q3(a), where the damping coefficient, c 10N.s/m and the spring constan k = 20N/m. When displaced from the equilibrium position, the mass is subjected to fre vibration response which can be described by the pendulum motion: d2x dx m + c + kx = 0 dt2 dt where x is the horizontal displacement from the equilibrium position and t is time. Th displacement (x) as a function of time t is given below, where the initial velocity y(t=0) zero. - x(t) t (s) x (m) 0.005 0.005 0.005 -0.0575 -0.08875 10 15 20 Figure Q3(a) i) Assume y = , reduce the system to first order differential equation. ii) Determine the first order differential equation over the time period of Osts 20
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
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Chapter1: Functions And Models
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Transcribed Image Text:a) A mass, m = 200N is attached to the free end of a vertical spring as shown in
Figure Q3(a), where the damping coefficient, c 10N.s/m and the spring constant,
k = 20N/m. When displaced from the equilibrium position, the mass is subjected to free
vibration response which can be described by the pendulum motion:
d2x
m at?
dx
+ kx = 0
dt
where x is the horizontal displacement from the equilibrium position and t is time. The
displacement (x) as a function of time t is given below, where the initial velocity y(t=0) is
zero.
+ x(t)
x (m)
0.005
0.005
0.005
-0.0575
-0.08875
t (s)
10
15
20
Figure Q3(a)
i)
Assume y =
dt'
dx
reduce the system to first order differential equation.
ii) Determine the first order differential equation over the time period of Os t s 20s
seconds using the Euler's method. (CO2,PO2)(C3)
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