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(II) Figure 29 shows two examples of SHM, labeled $A$ and B. For each, what is $(a)$ the amplitude, $(b)$ the frequency, and $(c)$ the period? $(d)$ Write the equations for both $A$ and $B$ in the form of a sine or cosine.

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a. $$=2.5 \sin \omega t$$ $$A_{\mathrm{B}}=3.5 \mathrm{m}$$b. $$=0.50 \mathrm{Hz}$$$$f_{A}=0.25 \mathrm{Hz}$$c.$$\begin{array}{l}{\text { For } \mathrm{A} \text { is }\left[T_{A}=4 \mathrm{secs}\right.} \\ {\text { For } \mathrm{B} \text { is }\left[T_{B}=2 \operatorname{secs}\right.}\end{array}$$d. Equation for $A$ is $x=2.5 \sin 2 \pi(0.25) t$$$x=2.5 \sin 0.5 \pi t$$Equation for $B$ is$$y=3.5 \cos \pi t$$

04:52

Shital Rijal

Physics 101 Mechanics

Chapter 14

Oscillators

Motion Along a Straight Line

Motion in 2d or 3d

Periodic Motion

Cornell University

University of Washington

Simon Fraser University

University of Sheffield

Lectures

04:01

2D kinematics is the study of the movement of an object in two dimensions, usually in a Cartesian coordinate system. The study of the movement of an object in only one dimension is called 1D kinematics. The study of the movement of an object in three dimensions is called 3D kinematics.

02:18

In physics, an oscillation is the repetitive variation, typically in time, of some measure about a central value or between two or more different states. The oscillation may be periodic or aperiodic.

02:20

Figure $14-29$ shows two e…

03:41

(II) Figure $11-50$ shows …

01:28

Figure 11$-$51 shows two e…

03:07

02:24

The figure shows two examp…

00:36

The figure shows the displ…

01:25

a) Determine the period an…

06:27

Draw a graph showing the p…

00:45

Two SHMs are represented …

00:51

Two SHMs are represented b…

02:42

The graph below shows the…

04:22

01:38

Determine the amplitude, p…

03:40

1. Object Undergoing SHM A…

02:58

$\bullet$ The equation of …

00:26

What are the (a) amplitude…

03:53

The graph of one complete …

for this problem on the topic of oscillators, We are given a graph that shows two examples of objects executing simple harmonic motion, object and object B. For each of these objects. We want to find the amplitude, the frequency and the period of motion from the graph. And finally to write equations for both A and B. In the form of a sign, A co sign. Now for A, we can read that the amplitude of aids motion A. is 2.5 meters and a. B has a greater amplitude of three 0.5 meters. So those are the amplitudes for A. And be next. We want to find the frequency of motion. Now for a, the frequency is one cycle every four seconds. So the frequency of A is 0.25 per second Or 0.25 Hz. For me, the frequency is one cycle every two seconds. So F. B. The frequency of B is 0.5/s or zero 0.5 huts. For see, we want to find the period and the period is simply the reciprocal of the frequency. So the period of a is one over 0.25 Which is four seconds. And similarly for B, The period for B is one over 0.5 which is two seconds. And so we have the periods for A and B. Lastly we want to find the displacement as a sign. Of course in function. Now, object a has a displacement of zero and T is equal to zero. So it has a sine function and its displacement X. A. Um It written as a aptitude times sine of two pi times its frequency F. A times T. Since we know these values, we can write this as Its amplitude 2.5 m times you sign of a half times pi times T. For B, object B has a maximum displacement when T is equal to zero, so it has a call sign function, and so X. Be committed in the form A. B times co sign two pi times the frequency, F B times T, which we can write as 3.5 m times the call sign of Pie times T. And so we have the equations for A and be as required.

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