Hi All,
I have a question regarding mass spring system.
mẍ+kx=0 →(A) is an equation which represents mass spring system. It is a linear equation of second order. If I want to make it non-linear I make it like
mẍ+kx+k1(x^3)=0, i.e. I add another term k1(x^3). Why can’t I add k1(x^2) to (A) to make it non-linear?
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"Why can’t I add
"Why can’t I add k1(x^2) to (A) to make it non-linear?"
yes, you can.
In reply to "Why can’t I add by h_robert64
Mathematically we can, but not physically.
Well mathematically we can make it non-linear by adding a x^2 term but physically, the force would no longer be a restoring force. if we put in positive or negative values of x; that is displacement, we will always get a positive answer. So this means that force is not a restoring one. So we don't add X^2, instead we add odd powers like X^3 to make it non linear.