Question

Two springs with spring constants k1 and k2 are connected together. With mass m1 attached, the springs have

Answer 1

K1x1=k2x2=F
k2x2/k1=x1
F=keqx=keq(x1+x2)

sub.s in for x1:F=keq(k2x2/k1+x2)

sub.s in for F (in terms of k2 and x2)k2x2=keq(k2x2/k1+x2)

x2 is in every term:k2=keq(k2/k1+1)

multiply both sides by (k1/k2+k1)
keq=(k1/k1+k2)k2
keq=(1/k1+1/k2)−1