Write out the expression for the vertical velocity

[leonne]

Homework Statement

Given z(t) as above, write out the expression for the vertical velocity

Homework Equations

z(t)=Asin(vt)
where z(t) is the vertical position of a test particle, A is the amplitude of its motion,
and t = 0 is the time when the particle is at the midplane

The Attempt at a Solution

So I just take the the derivative right? I am given position so if i take the derivative of position that give velocity. so is the answer v(t)=Avcos(vt)?

 

[Dick]

I don't see any problem with that.

 

[leonne]

cool thxs o one more thing idk if this matters the formula i was given is general solution for a differential equation. idk if that changes anything or if I need to use the original equation or something

 

[Dick]

The derivative of z(t)=Asin(vt) is Avcos(vt). Nothing can really change that. Whether that solves the original problem is hard to say until you tell what it is.

 

[leonne]

In class, we showed that the vertical equation of motion for a uniform density disk is
((d^2z)/dt^2) +v^2 z=0
The solution of this differential equation can be written as
z(t) = A sin(vt)
where z(t) is the vertical position of a test particle, A is the amplitude of its motion,
and t = 0 is the time when the particle is at the midplane (z = 0).
Just seems a little to easy that you just take the derivative, but than again i seem to always over complicate the problems lol, but ill just take it like i said before thxs

 

[Dick]

I'm not sure exactly what physics the situation is trying to derive, but sure, z(t)=A*sin(vt) solves that differential equation, and if z(t) is the vertical displacement then d(z(t))/dt is the vertical velocity. I'm not sure how you could complicate it.

 

[leonne]

kk thxs i thought maybe you do something different casue its vertical or somthing