How to find acceleration or displacement with respect to time?

[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?

 

[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.

 

[dextercioby]

Plus a constant (the ODE is nonhomogenous).

Daniel.

 

[sid_galt]

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

 

[marlon]

$$a(x)= kx + 1$$
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?

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

 

[dextercioby]

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

Daniel.