Skip to main content
Ch 14: Periodic Motion

Chapter 14, Problem 14

For the oscillating object in Fig. E14.4

, what is (a) its maximum speed?

Verified Solution
Video duration:
5m
This video solution was recommended by our tutors as helpful for the problem above.
410
views
Was this helpful?

Video transcript

Hey everyone in this problem we have a position time graph of a particle attached to a horizontal spring shown in the image. Okay but we're asked to find the objects. Maximum speed. Alright so let's recall the maximum speed V max is given by plus or minus the amplitude times. Oh my God. Alright so what we need to do is we need to find the amplitude A and we need to find omega in order to calculate our maximum speed. Okay let's start with the amplitude. Okay now the amplitude A is going to be the maximum displacement From x equals zero. So if we look at our graph, okay the maximum value on our graph is at 4cm. Okay the minimum is at negative four cm. Okay and so the maximum displacement from x equals zero. It's going to be this distance of four cm. Equivalently this distance of four centimeters or amplitude A is going to be equal to four centimeters and just be careful. It's not that entire distance from the maximum to the minimum. It's the distance, maximum displacement from X equals zero to that. Either maximum or minimum. Okay so it's four centimeters not eight. Alright so we found our max displacement. Now we need to find omega. Okay now one thing when we get graphs of position time like this, we want to think of things that are simple to find off our graph and one thing that is relatively simple to find a bar graph is the period T. Okay so we want to find omega we know that we'll be able to find our period T. Okay so we're called that we can relate omega to the period T. Through omega is equal to two pi over tea. Alright so let's go to our diagram and try to figure out this period. Okay so we want to go through and pick points that are in the same spot of the cycle. Okay? We want to go through an entire cycle and choose the next point. That's at the same position. Alright so let's pick the point here on the y axis. So at T equals zero. We have positioned four centimeters. Now we want to go through one complete oscillation, one complete cycle. So we're gonna go all the way down to the minimum, back up to the maximum and choose this corresponding point here. Okay, that's one complete cycle. And our period is going to be the time between those two points. Hm. Alright so we'll see that our period t. Okay we're starting at zero seconds and we're going all the way up to approximately 12.5 seconds. So our period T. Is going to be 12.5 seconds. Just that time it takes to complete one oscillation or one cycle. Alright so now we can find our angular frequency omega. It's going to be two pi over the period 12. seconds. Which gives an omega value of 0.5 0- x five radiance per second. So we have a we have omega. Now we can calculate that maximum speed we're looking for using a omega. So R V max Again is a omega which is going to be equal to four cm times the angular frequency. 0.50- radiance per second. Which gives a maximum speed of 2.1 centimeters per second. Okay. Now if we look at our answer traces we see that they're all in meters per second. We have centimeters per second. And this is why it's important to carry your units throughout the problem. Okay. The graph we were given gave us the position in centimeters. Okay? Which is what we wrote out when we had our amplitude a Okay, Which is how we get to the units of centimeters per second for speed. V. Okay. So it's important to write out those units so that when you work out the problem, you know what unit you have for your final answer? Okay. Now we want to convert this to meters per second to compare to these answer choices. Okay this is gonna be 2.1 centimeters per second. Okay. And we can multiply by one m per 100 centimeters. The centimeters will cancel. Okay? And we're left with 0. approximately meters per second. Okay? So if we look at our answer choices we see that we have be the objects. Maximum speed is going to be 0.02 m/s. Thanks everyone for watching. I hope this video helped see you in the next one.
Related Practice
Textbook Question
A small block is attached to an ideal spring and is moving in SHM on a horizontal frictionless surface. The amplitude of the motion is 0.165 m. The maximum speed of the block is 3.90 m/s. What is the maximum magnitude of the acceleration of the block?
2672
views
Textbook Question
A 0.500-kg glider, attached to the end of an ideal spring with force constant k = 450 N/m, undergoes SHM with an amplitude of 0.040 m. Compute (b) the speed of the glider when it is at x = -0.015 m.
622
views
Textbook Question
A 0.500-kg glider, attached to the end of an ideal spring with force constant k = 450 N/m, undergoes SHM with an amplitude of 0.040 m. Compute (e) the total mechanical energy of the glider at any point in its motion
739
views
Textbook Question
For the oscillating object in Fig. E14.4

, what is (b) its maximum acceleration?

836
views
Textbook Question
A mass is oscillating with amplitude A at the end of a spring. How far (in terms of A) is this mass from the equilibrium position of the spring when the elastic potential energy equals the kinetic energy?
1655
views
Textbook Question
A thrill-seeking cat with mass 4.00 kg is attached by a harness to an ideal spring of negligible mass and oscillates vertically in SHM. The amplitude is 0.050 m, and at the highest point of the motion the spring has its natural unstretched length. Calculate the elastic potential energy of the spring (take it to be zero for the unstretched spring), the kinetic energy of the cat, the gravitational potential energy of the system relative to the lowest point of the motion, and the sum of these three energies when the cat is (a) at its highest point.
1795
views