Oscillations and Relativity

Lots of problems...

1) There is a simple pendulum with L = 0.61m and it is in a car that is moving witn an accelartion of 3.2 m/s. How would one find the period?

So far I have T = 2*pi*(L/g)^1/2, but I don't know where to factor in the acceleration... an explaintion would be helpful.

Answer is 1.5 seconds.

2) An object has a rest density is given as "n", how fast would the object have to move in order to have a denisty of 1.088n ?

I'm thinking that mass would increase and volume would decrease.. I get an answer of 0.393 * speed of light .. but it's apparently 0.878 * speed of light.

3)How fast does a particle have to move to have its kinetic energy of a particle equal to its rest energy?

When I saw this I thought it had to be the speed of light... but once again I'm wrong and its 0.87 * speed of light. I don't think this is possible... so an explaination would help.

Thanks :<

2) keep in mind length contraction
3) An object can have infinite energy as it approaches C. The rest energy is only a small component, E^2 = p^2c^2 + m^2c^4, where m is rest mass.

>>2
2) I went back and tried it with length contraction.. but I still can't get the answer. I must be doing something retarded. Please explain.

3) Ok I used  " E^2 = p^2c^2 + m^2c^4 " equated p^2c^2 = m^2c^4. Then solved for v where p = mv.

Did some algebra and got that v = [1/sqrt(2)] * C. Since I equated p^2c^2 = m^2c^4 which was for E^2, I took the root of that again and got 0.84... a bit off of the answer. Is my method correct?

Thanks for the help.