5. For a simple seismograph as shown in Figure Q5 below, the co-ordinate X₁ measures horizontal ground motion and co-ordinate X measures the position of the mass m relative to the frame of the seismograph. The mass m = 1 kg, the spring stiffness k = 10 Nm-¹ and the coefficient of the damper c = 2 Nsm-¹. Starting from rest, the seismograph is subjected to an oscillatory ground motion given by X₁ = (10sin2t) mm. For the mass m,

Elements Of Electromagnetics
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Author:Sadiku, Matthew N. O.
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5. For a simple seismograph as shown in Figure Q5 below, the co-ordinate
X; measures horizontal ground motion and co-ordinate X measures the
position of the mass m relative to the frame of the seismograph.
The mass m = 1 kg, the spring stiffness k = 10 Nm-1 and the coefficient
of the damper c = 2 Nsm-¹.
Starting from rest, the seismograph is subjected to an oscillatory ground
motion given by X; = (10sin2t) mm.
For the mass m,
(a) set up the equation of motion,
(b) calculate the amplitude of the steady state response, and
(c) develop an equation describing the amplitude of steady state oscillation
as a function of time.
To
Figure Q5
m
Transcribed Image Text:5. For a simple seismograph as shown in Figure Q5 below, the co-ordinate X; measures horizontal ground motion and co-ordinate X measures the position of the mass m relative to the frame of the seismograph. The mass m = 1 kg, the spring stiffness k = 10 Nm-1 and the coefficient of the damper c = 2 Nsm-¹. Starting from rest, the seismograph is subjected to an oscillatory ground motion given by X; = (10sin2t) mm. For the mass m, (a) set up the equation of motion, (b) calculate the amplitude of the steady state response, and (c) develop an equation describing the amplitude of steady state oscillation as a function of time. To Figure Q5 m
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