Classical mechanics - mass/spring attached to moving support

You said that the support oscillates at a frequency of wa, (omega times a). What is a? Was it just a miss-type?

Also, for part a, I don't think you integrated cosine correctly. why does t^2 end up on the denominator of the integrated function?

 

Unfortunately, its not so simple. This equation: ma*=kAcos(ωt)-mg is wrong. It assumes that the only contribution to the relative acceleration is due to the support moving, but the mass will have motion also.

Sorry I didn't say this in my first post, but I had only looked through your work for obvious errors. Another reason to be suspicious of your answer is that as t gets larger, x approaches minus infinity! This is not a realistic solution, so it should hint to you that your assumptions were incorrect.

The true equation representing this situation is an inhomogeneous 2nd-order differential equation. To get the equation, just think about the position of the support and position of the mass as two separate variables (to begin with), and you know the equation for the force on the mass due to relative distance between mass and support. Then you can see the position of the mass as the dependent variable and the position of the support as simply the inhomogeneous part of the equation. From there you need to solve the complementary function and particular integral, which eventually gives you the solution.

There are probably short-cut ways of doing all this, but this is the standard way that is shown in most textbooks.