Capacitors Charge & Maximum Height of an object

klueless

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Here are the two of my problems I am having difficulties with. I decided to include both of these into a single thread, because they are both quite basic exercises. Both of these must also be quite simple to solve when I understand some basic principles, but since I am new to differential equations and the teaching hasn't been so good, I have really no clue how to solve these. Help much appreciated!

Thank you guys.
 
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View attachment 13461

Here are the two of my problems I am having difficulties with. I decided to include both of these into a single thread, because they are both quite basic exercises. Both of these must also be quite simple to solve when I understand some basic principles, but since I am new to differential equations and the teaching hasn't been so good, I have really no clue how to solve these. Help much appreciated!

Thank you guys.
For #2, can you do the following integration:

\(\displaystyle \displaystyle{q(t) \ = \ \int i(t) dt \ = \ \int\left [2 + sin^2(3t)*cos(3t)\right ] dt }\)

You need to post problem#3 in a separate thread. You will first need to derive the expression for the height of the object from the information given. Are you familiar with Galileo's equations for projectile motion?
 
Yes and by integrating i get this:

2t + 1/9 sin^3 (3t) + constant


I will ask more help on #3 in a different thread as you adviced, but let's consider this #2 now for a while.

The thing I'm not seeing is what to do with this integral and what does it actually mean. If it was previously derived, why would I want to get rid of this form where I can actually see the rate of change and what does this integrated form actually show me.
 
Yes and by integrating i get this:

2t + 1/9 sin^3 (3t) + constant


I will ask more help on #3 in a different thread as you adviced, but let's consider this #2 now for a while.

The thing I'm not seeing is what to do with this integral and what does it actually mean. If it was previously derived, why would I want to get rid of this form where I can actually see the rate of change and what does this integrated form actually show me.
What does q(t) mean in this problem?
 
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