# Homework Help: HELP A problem on oscillation

1. Jan 14, 2009

### Kudo Shinichi

HELP!!!A problem on oscillation

1. The problem statement, all variables and given/known data
the equation of motion of an object is y(t)=2.0cos(0.5t+pi/4)meter
a) Find its maximum acceleration and maximum speed, and its position at the time of these maxima.
b) what is the speed of the object when it is +1.2m from its equilibrium position?
c) what are the kinetic potntial and total energies at that point?

3. The attempt at a solution
a) for this part I don't reall understand what does the question mean by the maximum, is it when cos equals to 1?
b) derive 2.0cos(0.5t+pi/4), which equals to -2sin(0.5t+pi/4)*0.5=-1sin(0.5t+pi/4)
then plug the 1.2 into the unknown variable, which equals to -sin(0.5*1.2+pi/4)=-0.98 I don't really think it is the correct solution for this part
c) I have to find out the correct v from part B and plug into both kinetic and potential energy equation, but I have one more problem here, which is how do i get mass for this question?
P((1/2mv^2)i) + K(1/2mv^2)i) = P((1/2mv^2)f) + K(1/2mv^2)f)

Thank you for helping me.

2. Jan 15, 2009

### AEM

Re: HELP!!!A problem on oscillation

(a)When you differentiate to find the velocity, you will, as you know get a sine function. The maximum of the speed occurs when the sine function is equal to 1. Similarly when you differentiate once more you get a cosine function and the maximum of the acceleration occurs when the cosine function is equal to 1, so you were on the right track.
Notice that you will have to figure out the time it takes for sine and cosine to get to 1to fully answer the question.

(b) Here the problem asks what is the speed WHEN the object is a 1.2m, but you substituted meters for time! That is not correct. You need to figure out how long it takes for the object to reach 1.2m

(c) Not every answer is in a numerical form. If they don't give you the mass, then just express your answer in terms of m.