Hey there! We receieved your request
Stay Tuned as we are going to contact you within 1 Hour
One of our academic counsellors will contact you within 1 working day.
Click to Chat
1800-5470-145
+91 7353221155
Use Coupon: CART20 and get 20% off on all online Study Material
Complete Your Registration (Step 2 of 2 )
Sit and relax as our customer representative will contact you within 1 business day
OTP to be sent to Change
Dear apraitm,
Let k be the spring constant of the spring.
Here reduced mass concept will be applicable. so reduced mass of the system is M= mm'/(m+m')
or this solution, I will already assume that all motion takes place in the x-direction. So, I can write Newton's second law as:
Where Fx is the total force (there is only one in this case anyway). Please forgive me, but I am going to drop the "in the x-direction" notation since EVERYTHING is only in the x-direction. The force from the spring is:
Remember that this spring has zero natural length, so the x position IS the "stretch". Putting this together, I get:
Here I wrote acceleration as the second time derivative of position. If that is something completely foreign to you, don't worry - you will see this later maybe. Anyway, what I have here is a differential equation. How do you solve a differential equation? There are lots of strategies, but I find the best one is to guess. Yes, just guess a solution and see if it works. First, let me re-write the differential equation:
If you look at this equation, it says "take the derivative with respect to time twice and get something times the original function" (really, it says that, you might have to listen closely). Once function that does that is ....cosine. So, let me try the function:
Where A and ? are constants. Let me take the first derivative:
And now the second derivative:
So this means that:
ACCELERATION=Kx(m+m')/(mm')
We are all IITians and here to help you in your IIT JEE preparation. All the best. If you like this answer please approve it.... win exciting gifts by answering the questions on Discussion Forum Sagar Singh B.Tech IIT Delhi sagarsingh24.iitd@gmail.com
We are all IITians and here to help you in your IIT JEE preparation. All the best.
If you like this answer please approve it....
win exciting gifts by answering the questions on Discussion Forum
Sagar Singh
B.Tech IIT Delhi
sagarsingh24.iitd@gmail.com
Get your questions answered by the expert for free
You will get reply from our expert in sometime.
We will notify you when Our expert answers your question. To View your Question
Win Gift vouchers upto Rs 500/-
Register Yourself for a FREE Demo Class by Top IITians & Medical Experts Today !