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Solution General solution c(t=A cos wnt+B sin wnt or xc(t)=Csin(unt+φ) Initial conditions x(0)=x0x(0)=io Solution w(t=o cos wnt+-sin wnt or 1r0 a(t)=va5+(co/wn)sin(wnt +tan( ))Solution General solution x(t) = A cos ωnt + B sin ωnt or, x(t) = C sin(ωnt + φ) Initial conditions x(0) = x0 x˙(0) = ˙x0 Solution, x(t) = x0 cos ωnt + x˙0 ωn sin ωnt or, x(t) = q x 2 0 + ( ˙x0/ωn) 2 sin(ωnt + tan−1 ( x0ωn x˙0 )) 2
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