You can adapt the code based on the function you have. Free vibration of SDOF systems (undamped) draws displacement velocity and acceleration with respect to time can be calculated below.

m = 2;
k = 8;
w = Sqrt[k/m];

u = DSolve[{y''[x] + (w^2)*y[x] == 0, y[0] == 3, y'[0] == 5}, y[x], x][[1, 1, 2]] // Simplify

3 Cos[2 x] + 5 Cos[x] Sin[x]

v = D[u, x]

5 Cos[x]^2 - 5 Sin[x]^2 - 6 Sin[2 x]

a = D[v, x]

-12 Cos[2 x] - 20 Cos[x] Sin[x]

p1 = Plot[u, {x, 0, 2}, AxesLabel -> {"time in secs", "displacement"},
    PlotStyle -> {Thickness[0.01]}];
p2 = Plot[v, {x, 0, 2}, AxesLabel -> {"time in secs", "velocity"}, 
   PlotStyle -> {Thickness[0.01]}];
p3 = Plot[a, {x, 0, 2}, AxesLabel -> {"time in secs", "acceleration"},
    PlotStyle -> {Thickness[0.01]}];
{p1, p2, p3}

You can adapt the code based on the function you have. Free vibration of SDOF systems (undamped) draws displacement velocity and acceleration with respect to time can be calculated as in below code. Some demos can be found at Wolfram demonstrations site. demo1 demo2 demo3

m = 2;
k = 8;
w = Sqrt[k/m];

u = DSolve[{y''[x] + (w^2)*y[x] == 0, y[0] == 3, y'[0] == 5}, y[x], x][[1, 1, 2]] // Simplify

3 Cos[2 x] + 5 Cos[x] Sin[x]

v = D[u, x]

5 Cos[x]^2 - 5 Sin[x]^2 - 6 Sin[2 x]

a = D[v, x]

-12 Cos[2 x] - 20 Cos[x] Sin[x]

p1 = Plot[u, {x, 0, 2}, AxesLabel -> {"time in secs", "displacement"},
    PlotStyle -> {Thickness[0.01]}];
p2 = Plot[v, {x, 0, 2}, AxesLabel -> {"time in secs", "velocity"}, 
   PlotStyle -> {Thickness[0.01]}];
p3 = Plot[a, {x, 0, 2}, AxesLabel -> {"time in secs", "acceleration"},
    PlotStyle -> {Thickness[0.01]}];
{p1, p2, p3}