00:01
All right, so we have a particle undergoing simple harmonic motion, and we're told the position as a function of time is given by 5 .3 times the cosine of 4 .2 t minus 1 .9.
00:16
So 4 .2, presumably this is like radiance per second, times t plus, so plus or minus, minus 1 .9 radiance.
00:29
And the amplitude, sorry, is in meters.
00:33
So this should be 5 .3 meters.
00:36
So this is our position as a function of time.
00:39
And we want to know what is the position of the object at 2 .6 seconds.
00:44
So let's just plug this in.
00:48
This would be 5 .3 meters times the cosine of 4 .2 radians per second times 2 .6 seconds minus 1 .9 radiance.
01:06
So if you're doing this along with me in your calculator, make sure your calculators in radiance rather than degrees.
01:12
So we got 4 .2 times 2 .6 minus 1 .9.
01:17
Take the cosine of that, multiplied by 5 .3.
01:20
You should get something like negative 4 .87 meters.
01:26
And then we also want to know what is the velocity and basically the acceleration at the same time.
01:33
So the velocity as a function of time is just going to be negative 5 .3 meters times 4 .2 radiance a second times the sign of the same argument.
01:49
So 4 .2 radians a second times 2 .6 seconds minus 1 .9 radians.
02:00
So if we do that, 4 .2 times 2 .6 minus 1 .9, and we take the sign of that, and then multiply by 5 .3 times 4 .2...