Simple harmomic motion

What is the equation for the motion?

What do you call the time derivative of the equation of motion?

 

ad i) Do you know the equation for simple harmonic motion - i.e. the relation between position and time? Solving this part is just a matter of solving this equation for y = 3.

ad iv) The same story. Just use the equation* for velocity of simple harmonic movement and solve for v = 6 m/s to get the time and use the equation in i) to get the position.

*you might get this one by differentiating the equation in i)

don't forget the minus sign - do you know what its significance is?

 

i) is correct.
ii) is wrong. To get a velocity differentiate the x=asinwt wrt t.

 

Ok for the first one , you need to form a equation and then solve it . It is given that the y - position is 0 at t=0. w=100pi and A=0.04m (always work with s.i units) . Using these info we can form the equation , y=A Sin(wt) , in this case it would be 0.03=0.04Sin((100pi)(t)) , solving for this will result in the answer!!!

 

Sorry about the double post

 

For part 2 , once again we need to form a equation, this time , we need to form the equation for velocity. Which would be v=-wACos(wt) (it is cos because at origin , y=0) From i) you have your t which you can sustitute into the equation and solve it!!

 

Ok for part 3) , you need to form another equation. The equation would be a=-W^2ASin(wt). Using the ans from part 1) , you can sole the equation and get your ans!!!

 

just for you info imy786 , v=Aw and a= Aw^2 give you the maximum velocity and maximum acceleration.

 

imy786 it depends on the situation of the question . Sketch a simple y vs t and v vs t graph side byside ,You will then see whether it is - or +

 

I use cos instead of sin in my equations as my phase angle is 0 as it starts from y=0 at t=0. If u wish u can also use y= A Sin(wt + phi) then v= -AWCos(wt + phi) .Ooops my bad . Sorry .Like i said just draw a graph and you will see what to do.