00:01
All right, so we're told we have a mass of 580 grams, so 0 .58 kilograms, and it's attached to a spring and set into simple harmonic motion.
00:12
And the equation describing this is something like 0 .34 meters times the cosine of 10 radians per second times t.
00:27
And so we want to, first off, determine the amplitude of oscillation.
00:32
So this is easy.
00:34
The amplitude is just going to be the coefficient of the cosine term in here.
00:37
So 0 .34 meters or 34 centimeters.
00:41
And now we want to know the force constant for the spring as well.
00:45
Well, one thing we do know is that the angular frequency of the spring is given by the square root of k over m.
00:53
So we can see the spring constant is going to be omega squared, times m and omega is the coefficient of t in this equation so it'll be like a hundred you know radiance squared per second squared times 0 .5 8 kilograms so this will be 58 and then we could alternative right this right this is 58 newtons per meter so that's our spring constant and then part c we want to know the position of the mass after it's been oscillating for half a period so of course it will help to know what the period is.
01:27
The period is going to be 2 pi divided by the angular frequency, so like pi over 5 seconds.
01:36
And so after half a period, of course, this is just pi over 10 seconds.
01:43
So if we plug that into our equation for x to t, plug in pi over 10, well, we'll get a 0 .34 meters times the cosine of 10 times pi over 10.
01:54
So just pi...