# How to find acceleration or displacement with respect to time?

1. Apr 8, 2005

### sid_galt

$$a(x)= kx + 1$$
where $$a(x)$$ is acceleration with respect to displacement along the x-axis and $$x$$ is the displacement itself while k is the constant.

How to find acceleration or displacement with respect to time?

Last edited: Apr 8, 2005
2. Apr 8, 2005

### dextercioby

Use the definition of acceleration to write the ODE.Depending on that sign of "k",the answer for x(t) is a linear comb.of complex or real exponentials...

Daniel.

3. Apr 8, 2005

### dextercioby

Plus a constant (the ODE is nonhomogenous).

Daniel.

4. Apr 8, 2005

### sid_galt

I can't figure out the ODE. Can you help me?

5. Apr 8, 2005

### marlon

acceleration is the second derivative of x wtr to time :

$$\ddot{x} = kx + 1$$

$$\ddot{x} -kx -1 = 0$$

Can you solve it from here. You will need to set up the associated caracteristic equation and based upon the sign of k you will get a linear combination of exponentials or complex exponentials

marlon

6. Apr 8, 2005

### dextercioby

The nonhomogeneity part is usually left in the RHS...

Daniel.