Simple Harmonic Motion - Velocity EQ.

[Masri]

Homework Statement

x = 0.20m*sin(0.44 rad/s * t)


Write the equation for the velocity of this object. Find the velocity at t = 4:0 s.

Homework Equations

The Attempt at a Solution

well, i know that v(t)= - wAsin(wt +$$\phi$$)

and we know the w = 0.44 rad/s
A = 0.20 s
t=4

so it i plugged the numbers in but the answer came wrong..

and the answer in the book says ...
v= 0.088 m/s* cos ( 0.44 rad/s * 4 s)

v= - 1.7 *10^-2 m/s


well first where did he get that equation from ? 2nd if we actually calculated (v= 0.088 m/s* cos ( 0.44 rad/s * 4 s) ) it won't give us v= - 1.7 *10^-2 m/s

so if somone could please help me out with this one... any help would be appreciated ,

Thanks!

 

[xiaoB]

and the answer in the book says ...
v= 0.088 m/s* cos ( 0.44 rad/s * 4 s)

v= - 1.7 *10^-2 m/s

As i know, the calculation of the book was using radian(0.44) changed to degree(25.12⁰).So,the answer would get -0.01655 m/s.

But for me, normally we usage radian.

 

[Masri]

but where did he get that formula from ?

 

[eczeno]

hello,

your equation for the velocity is incorrect. can you show what you did to derive it?

 

[xiaoB]

but where did he get that formula from ?

(0.44rad/pi)x180⁰=25.12⁰

 

[Masri]

hello,

your equation for the velocity is incorrect. can you show what you did to derive it?

it is actually given to us like this in our formula sheet . (am talking about the on i used, not the one the book )


thanks xiaoB, but i was talking about the velocity equation that the book used

 

[xiaoB]

hello,

your equation for the velocity is incorrect. can you show what you did to derive it?

Hi,eczeno!

Actually he correct because the sine has the phase ∅.

 

[eczeno]

if the formula you gave for the position is correct, then your velocity is incorrect.
v = dx/dt. take the derivative of x to find v.

notice the solution has cosine where you have sine; the solution given is correct.

 

[xiaoB]

it is actually given to us like this in our formula sheet . (am talking about the on i used, not the one the book )


thanks xiaoB, but i was talking about the velocity equation that the book used

You just derive this x = 0.20m*sin(0.44 rad/s * t) respected for t :

dx/dt=V.

 

[Dick]

Hi,eczeno!

Actually he correct because the sine has the phase ∅.

No, it's not correct. The derivative of A*sin(wt) is wA*cos(wt).

 

[xiaoB]

No, it's not correct. The derivative of A*sin(wt) is wA*cos(wt).

Yes ! the derive should be this wA*cos(wt) .

But if v(t)= - wAsin(wt + ∅) the sin(wt + ∅) for the phase ∅ is 90⁰ so the sin(wt + 90)=cos(wt).

Therefore,v(t)= - wAsin(wt + ∅) nothings going wrong.

 

[eczeno]

Yes ! the derive should be this wA*cos(wt) .

But if v(t)= - wAsin(wt + ∅) the sin(wt + ∅) for the phase ∅ is 90⁰ so the sin(wt + 90)=cos(wt).

Therefore,v(t)= - wAsin(wt + ∅) nothings going wrong.

of course the addition of the proper phase will turn cos into sin, but there is no phase specified in the attempted solution, so it is incorrect.

this is really only adding unnecessary confusion to a relatively simple problem. the derivative of sin is cos; this gets us directly to the correct solution without needing to worry about the phase.

 

[Dick]

Yes ! the derive should be this wA*cos(wt) .

But if v(t)= - wAsin(wt + ∅) the sin(wt + ∅) for the phase ∅ is 90⁰ so the sin(wt + 90)=cos(wt).

Therefore,v(t)= - wAsin(wt + ∅) nothings going wrong.

If I were first learning simple harmonic motion, that sort of approach to solving the problem would make me quit physics. That's what's going wrong.

 

[xiaoB]

If I were first learning simple harmonic motion, that sort of approach to solving the problem would make me quit physics. That's what's going wrong.

Oh!thanks.I not think so...