x1 = (a/4)*Cos[w1 t]  +  v0/(2 w1) Sin[w1 t]  +  
        a/4 Cos[w2 t]  +  v0/(2 w2) Sin[w2 t]

v1 = D[x1, t]

x2 = (a/4)*Cos[w1 t]  +  v0/(2 w1) Sin[w1 t]  -  
        a/4 Cos[w2 t]  -  v0/(2 w2) Sin[w2 t]

v2 = D[x2, t]

t1 = (1/2) m v1^2

t2 = (1/2) m v2^2

a = 1

v0 = 1

m = 200

k = 1

w1 = Sqrt[k/m]*1.

tau1 = 1. *(2 Pi/w1)

w2 = Sqrt[3 k/m]*1.

tau2 = 1.0*(2 Pi/w2)

Plot[x1, {t, 0, (6  Pi)/w1}]

Plot[x2, {t, 0, (4  Pi/w1)}]

Plot[t1, {t, 0, 100}]

Plot[t2, {t, 0, 100}]

Plot[t1 + t2, {t, 0, 100}]

U =  (k/2)* (x1^2  +  x2^2  + (x2 - x1)^2)

Plot[U, {t, 0, 100}]

Plot[U + t1 + t2, {t, 0, 100}]