Maximum Acceleration

sejr

Helping a friend out with some physics 1 mid-semester and It's been a little since I have had a physics course.... so the question is

"If a 30 g bird lands on a slender branch where it oscillates up and down with simple harmonic motion of amplitude 3.00 x 10^-2m and period 1.2 s"...

trying to find an equation to solve for max acceleration, expressed as a fraction of the acceleration of Gravity as well as maximum speed... any help would really be appreciated and thanks a lot to anyone that reads this

rock.freak667

SHM is defined as

a= -ω²x


Thus a will be max when x (displacement) is maximum. So at what value of x will the displacement be maximum?

sejr

I don't have a key and I feel like I may be way off but here is what I have so far

f= 1/t so F=.83 Hz

A= (2(3.14)f)^2 x
so A=27x

then for X,

X=Acos2(3.14)f(t)

sejr

wouldn't it be 3?

sejr

or would it be 6? I am confused in what to do with amplitude, if amplitude is 3 cm, that would mean peak to trough is 6 cm? Correct? Is that what I would go with?

sejr

Its asking for the max speed and acceleration of the bird, the thing that throws me off is I don't know if it is asking for the speed the bird landed on the branch or the speed which it actually oscillates

rock.freak667

Right and the maximum value of X is A.

sejr

Ok great, A as in amplitude or acceleration... sorry, thanks again

rock.freak667

A as in amplitude.

sejr

So then, would speed maximum or minimum when the finch hits max acceleration?

rock.freak667

Well when your displacement is zero, you would have maximum velocity.

Remember the bird is landing from some height. So as it hits, it will be at maximum velocity.

If we go back to your equation for displacement x=Asin(ωt), how would you find velocity from this?

sejr

makes sense, since the bird has yet to transfer its energy to the branch... Plug in amplitude -sin and multiply with the angular force times time period...?

So to get this straight, and I really appreciate all of this,

A as in amplitude
A= (2(3.14)f)^2 x
so A=27x

I would plug A= 27x and then solve for X which would be my maximum acceleration? In this case 3=27x so x would be 9 cm/s

Maximum Velocity would be the moment before impact?

The last thing it asks

sejr

is to express it as a fraction of the acceleration of gravity, so just 9cm/s^2?

rock.freak667

No, if x=Asin(ωt), how would you get velocity? Hint: What is the definition of velocity?




You can express the acceleration as a fraction of gravity as both are acceleration terms. If you want to express velocity in terms of gravity then your units will not make too much sense.