A machine part is undergoing SHM with a frequency of 4.00 Hz and amplitude 1.80 cm. How long does it take the part to go from x = 0 to x = -1.80 cm ?

Video transcript

Hey everyone in this problem. A sewing needle performs simple harmonic motion with an amplitude of 2.3 centimeters and a frequency of 20 hertz. Okay. We're asked to determine the time taken to move from y equals zero to y equals 2.3 centimeters. All right, so let's think about this. Okay, we have simple harmonic motion with an amplitude of 2.3 cm. So we can imagine drawing this out. Okay, and if we're going to go from zero up to 2.3 cm, which we know is our amplitude, so it's gonna be the maximum of that curve. And we can imagine drawing up the rest of this curve and what I've drawn in these dotted lines. That would be one full period. Okay, to go all the way down up to the maximum, down to the minimum and back to zero. A one full period. We've stopped at this maximum. And what we'll see is that this is actually a quarter of the period. Okay, so this is going to be T over four. So from zero to an amplitude a. K. Because 2.3 centimeters is our amplitude. So to go from 00 to a that represents a quarter of the period. Alright, so the time taken that we're looking for to go from 0 to 2.3 centimeters is going to be T over four. Okay. All right. So in order to calculate the time taken, we need to find the period T. We're not given information about the period T but we are given the frequency and let's recall that the frequency is related to the period through the inverse. So we have that the frequency is equal to one over T. Mhm. Which tells us that the period T. Is equal to one over the frequency F. And in our case this is gonna be 1/20 hertz which gives us a period Of 0. seconds. Alright. So we've figured out our period T. And we know that the time taken to go from 0 to 2.3 centimeters is T over four. Okay so the time taken T over four is 04. Going to be 0.05 seconds divided by four. Which gives us a time of 0.0125 seconds. Alright so we were given the amplitude, we were told to find the time from 0 to 2.3 centimeters. Okay. And we just needed to figure out how that relates to the period. Okay. How far are we going through that period? We figured out that that was T over four and use our frequency to find our period And we found that the time it takes to go from 0 to 2.3 cm is 0.0125 seconds. That's answer. B. That's it for this one. I hope this video helped see you in the next one