Simple harmonic motion - initial acceleration

[Tzabcan]

Homework Statement

To work out the intial acceleration, do we just use the equation:

So at t = 0

We eliminate the wt inside the bracket, and are left with Aω^(2)sin(Φ + π)

Homework Equations

The Attempt at a Solution

The part which I'm not so sure on, is if i have values for Φ, do i literally treat π as it's true value or 180?

Say Φ = π/2 (just a random number)...and A= 9 and ω = 3

Will this give me the initial acceleration:

((9* 3^(2)) sin (π/2+ 180) = ((9*3^(2))sin(270)

?

But with my actual example i have, doing it this way gives me a huge massive negative number as the sin of 270 is -1 lol.

Thanks

 

[SteamKing]

Homework Statement

To work out the intial acceleration, do we just use the equation:

So at t = 0

We eliminate the wt inside the bracket, and are left with Aω^(2)sin(Φ + π)

Homework Equations

The Attempt at a Solution

The part which I'm not so sure on, is if i have values for Φ, do i literally treat π as it's true value or 180?

Say Φ = π/2 (just a random number)...and A= 9 and ω = 3

Will this give me the initial acceleration:

((9* 3^(2)) sin (π/2+ 180) = ((9*3^(2))sin(270)

?

But with my actual example i have, doing it this way gives me a huge massive negative number as the sin of 270 is -1 lol.

Thanks

So, you're saying that -81 is a 'huge massive negative number'? Does A have any units attached?

 

[Herman Trivilino]

Homework Statement

To work out the intial acceleration, do we just use the equation:

So at t = 0

We eliminate the wt inside the bracket, and are left with Aω^(2)sin(Φ + π)

What does it mean to "work out the initial acceleration"? To understand that question we need to know what is given. That's the reason for the template.

 

[J Hann]

It looks like pi (radians) was inserted in this equation to account for the negative sign.
For SHM if we omit the phase angle phi
x(t) = A sin w t
v(t) = A w cos w t
a(t) = - A w^2 sin w t = A w^2 sin (w t + pi)
Since sin (theta + pi) = - sin theta

 

[Tzabcan]

Well, what we have been given is ω = 2.5 x 10^3 s A = 1.8mm Φ = π/2

I'm just confused how I'm supposed to be using this equation.

Do i quite literally just do:

0.0018m * (2.5 x 10^3)^2 sin (π/2 +π) ?

And then take the inside to be sin (270)? or do i take it as 4.7? :s

Thanks

 

[Herman Trivilino]

And then take the inside to be sin (270)? or do i take it as 4.7? :s

270° ≈ 4.7 radians.

sin(270°) = -1

sin(4.7 rad) ≈ -1

So, to answer your question, yes. You can use either.

 

[Tzabcan]

270° ≈ 4.7 radians.

sin(270°) = -1

sin(4.7 rad) ≈ -1

So, to answer your question, yes. You can use either.

Oh haha, should've put it into the calculator and see for myself. Thanks :)

 

[Herman Trivilino]

Or, you could keep track of the units as you go, something you seem to not be doing. It will catch up with you!