When does potential energy convert to kinetic fastest in a spring-mass system?

[DDS]

A mass on a spring with a constant of 3.76 N/m vibrates, with its position given by the equation x = (4.55 cm) cos(3.70t rad/s). During the first cycle, for 0<t<1.70 s, when is the potential energy of the system changing most rapidly into kinetic energy? There are two solutions, enter both with the smaller one first.

B)What is the maximum rate of energy transformation?

I have taken the square of the function given, then i have found the derivate of the sqaured function. I then set the derivate equal to zero in order to find my max and min but i get the wrong answer.

As for b i have no clue where to even start

 

[DDS]

I have found that

2wt=N(pi)
t= N(pi)/ 2w

i have arbitrarely pluged in vlaues for pie to find times between my given domain, thus i have resulted with these solutions:

n(0)=0
n(1)=0.424
n(2)=0.848
n(3)=1.27
n(4)=1.69

if i plug in 5 for n i get a time that is to large for my interval thus these are the for possible times. However i have tried each combination of these times and they do no produce the right answer.

Can sumone please help me solve this problem?

 

[Doc Al]

This problem is already under discussion here:
https://www.physicsforums.com/showthread.php?t=78288