00:01
So here for part a, the period t is simply the reciprocal of the frequency.
00:04
This would be equaling to 1 over 2 .0 hertz.
00:09
This is giving us then 0 .50 seconds.
00:14
We have then part b, the angular frequency, equaling 2 pi times the frequency.
00:21
This would be equaling to 2 pi multiplied by 2 .0 hertz, giving us 4 pi radians per second.
00:31
Now, we're going to use energy conservation, 1 .5 times k a squared plus 1 .5 times kx initial squared, rather, this is equaling, plus 1 .5 mv initial x squared.
00:51
So essentially, the total potential energy that can be stored is equal to the currently stored, the current stored potential energy in the spring plus the initial energy.
01:05
Kinetic energy and so solving then we can eliminate that one half and we find that then k a squared equaling k x initial squared plus m the initial x squared or k is equaling then m omega squared we can solve for a and a is equaling then 5 .5 4 centimeters.
01:34
Again, this is, we're using x initial equaling negative 5 .0 centimeters, and we have the initial x velocity equaling negative 30 centimeters per second.
01:49
And so we can say then, then, we also know the mass equaling 0 .200 kilograms.
01:58
So for part d, then, we can calculate the phase constant, a cosine of finite...