The 38th problem: I'm not getting the result in the book (SHM problem)

[Pawn]

Homework Statement

The 38 problem:The result on the book is 10.6cm i keep getting 3.75

Relevant Equations

X(t)=A×cos(w×t)

 

[kuruman]

Please show your work so that we can figure out where you went astray.

 

[Pawn]

Please show your work so that we can figure out where you went astray.

Please show your work so that we can figure out where you went astray.

 

[erobz]

View attachment 314480

Type your work in Latex

 

[kuruman]

You are assuming that SHM is motion under zero acceleration. It is not. The velocity in SHM is not related to position and time by $v=\frac{x}{t}$. What are the correct expressions for position and velocity in SHM? Your textbook should have those.

And yes, please learn how to write equations in LaTeX. Meanwhile, please do no post pictures sideways.

 

[DaveC426913]

How can you get a displacement of 37.5 if the max amplitude is specified as 15?
(This is intended to inspire a sanity check. If you mentally draw this motion in your head, that may help you figure out where you're going wrong.)

 

[Pawn]

You are assuming that SHM is motion under zero acceleration. It is not. The velocity in SHM is not related to position and time by $v=\frac{x}{t}$. What are the correct expressions for position and velocity in SHM? Your textbook should have those.

And yes, please learn how to write equations in LaTeX. Meanwhile, please do no post pictures sideways.

The only other equation i have is the one for the velocity in an instant of time v(t)=-vmax × sin(w × t).

W-omega
And i don't know what LaTeX is.

 

[Pawn]

How can you get a displacement of 37.5 if the max amplitude is specified as 15?
(This is intended to inspire a sanity check. If you mentally draw this motion in your head, that may help you figure out where you're going wrong.)

3.75*

 

[DaveC426913]

3.75*

mm OK. Your notes say 3.75, though your problem statement says 37.5.
Not sure if you can still edit post #1.

 

[kuruman]

The only other equation i have is the one for the velocity in an instant of time v(t)=-vmax × sin(w × t).

W-omega
And i don't know what LaTeX is.

If your textbook really does not have an expression for the position as a function of time, look it up on the web.

To find how to use LaTeX to write and post equations, go here
https://www.physicsforums.com/help/latexhelp/
or click the link LaTeX Guide, lower left corner.

 

[Pawn]

If your textbook really does not have an expression for the position as a function of time, look it up on the web.

To find how to use LaTeX to write and post equations, go here
https://www.physicsforums.com/help/latexhelp/
or click the link LaTeX Guide, lower left corner.

Do you have any idea on how to solve it?

 

[hutchphd]

Knowing the period allows you to figure out ω. Knowing the position at t=0 allows you to figure out A. Then obtain x(t) for t=0.1s.

 

[Pawn]

Knowing the period allows you to figure out ω. Knowing the position at t=0 allows you to figure out A. Then obtain x(t) for t=0.1s.

How ?

 

[hutchphd]

Look in your book for the relation between T and ω. Tell me what it is

 

[Pawn]

Look in your book for the relation between T and ω. Tell me what it is

ω=2π/T

 

[hutchphd]

So in your equation for x $$x(t)=A\cos\frac {2\pi t} T $$ Now what is A?

 

[Pawn]

A is 15cm. Right?

 

[hutchphd]

so t/T is 1/8 for t=0.1s

 

[Pawn]

So in your equation for x $$x(t)=A\cos\frac {2\pi t} T $$ Now what is A?

But if we substitute the values we don't get the result that is in the book.

 

[kuruman]

Do you have any idea on how to solve it?

I have lots of ideas how to solve it, but I will back off and let @hutchphd take over. You're in good hands.

 

[hutchphd]

cos (pi/4)= ? ( that's 45deg)

 

[Pawn]

cos (pi/4)= ?

Do we substitute pi with the value 3.14

 

[hutchphd]

You prefer 2pi/8 ? see #18

 

[Pawn]

You prefer 2pi/8 ? see #18

No sorry i didnt realize it

 

[Pawn]

cos (pi/4)= ? ( that's 45deg)

0.70

 

[hutchphd]

So are you good? I got to go right now but let me know

 

[Pawn]

So are you good? I got to go right now but let me know

Yes thank you so much for helping me .