Solution:
Principle of superposition dictates that we can find the response of a systems which is being acted upon by a number of forces by vectorally adding their responses. Thus the force acting of the system may be assumed to be composed of two parts,
F =
Now we are given a SDOF undapmed system.
Respomse of such a system for a time period of a multi force system is given as:
For undapmed system,
The response could be depicted as:
Natural frequency fo the system is given as, wn = (k/m)0.5 = (1500/30)0.5 = 7.07 rad/s
Fo = 150, to = 1sec
Now for 0<t<t0
x(t) = (2x150/1500)(1-cos7.07(t-1)) = 0.2(1-cos7.07(t-1)) m
Now for t0<t<2t0
x(t) = (x150/1500)(1-cos7.07(t)) = 0.1(1-cos7.07(t)) m
From the principal of superposition,
x(t) = 0.1{ 2-cos7.07(t-1)-7.07cos(t) }
Comments:
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