Analyzing the Dynamics of a Cart Between Two Springs

[Vickitty]

I've been having troubles figuring out this question, because the cart is not actually attached to either spring nor always touching one. Any help would be appreciated.

A cart moves without friction between two springs, back and forth. Both springs have a spring contact of D = 72 N/m. At the time t = 0s, the cart is at position x = 0m, going towards the right with a speed of .36 m/s. It meets the right spring after a distance of d = 18 cm. The mass m of the cart is 2 kg. The mass of the springs can be ignored.
a) How long does the cart touch the right spring? (I simply calculated the period of the spring and got 1.047 s, but this is apparently incorrect?)
b) How much will the spring be compressed? (Not sure what to do here.)
c) At which location x will the acceleration be the largest? Give the maximal acceleration (This would just be the moment before the spring starts to push the cart back towards the center again, right? So d = 18 cm plus the amount the spring is compressed? Then use -kx = ma to determine what it is?)

Thank you!

 

[Chen]

a) I'm assuming you calculated the period of the simple harmonic motion. That is correct, but remember the mass is only going through half a cycle so the time of contact should be T/2.

b) Use conservation of energy:
$$\frac{1}{2}mv^2 = \frac{1}{2}kx^2$$

c) You are absolutely correct.

 

[Vickitty]

Thank you, that's a great help. I think I've got it now!