Calculate the period of a ball bouncing between two walls

[Like Tony Stark]

Homework Statement

A particle of mass $m$ moves with velocity $v_0$ and collides with the wall. Determine the period of oscillation if:
A) The collisions are perfectly elastic
B) The kinetic energy of the ball decreases 2 % with every collision. The period will be a function of the number of collisions.

Relevant Equations

$d=tv$

For A) I just have to calculate the time taken to travel from the middle to the wall and multiply that number by 4, since it travels the same distance 4 times.
$t=\frac{x_0}{v_0}$

B)The energy is an exponential function
$T(n)=T_0.(1-\frac{2}{100})^n$
So
$v^2={v_0}^2.(1-\frac{2}{100})^n$

Then I just have to replace that value in the formula from the previous exercise (taking into account that the latest expression is squared)

Is this right?

 

[haruspex]

Homework Statement:: A particle of mass $m$ moves with velocity $v_0$ and collides with the wall. Determine the period of oscillation if:
A) The collisions are perfectly elastic
B) The kinetic energy of the ball decreases 2 % with every collision. The period will be a function of the number of collisions.
Relevant Equations:: $d=tv$

For A) I just have to calculate the time taken to travel from the middle to the wall and multiply that number by 4, since it travels the same distance 4 times.
$t=\frac{x_0}{v_0}$

B)The energy is an exponential function
$T(n)=T_0.(1-\frac{2}{100})^n$
So
$v^2={v_0}^2.(1-\frac{2}{100})^n$

Then I just have to replace that value in the formula from the previous exercise (taking into account that the latest expression is squared)

Is this right?

Yes, that's a good approximation, but strictly speaking one oscillation will involve (if it starts in the middle) three different speeds.