# Maximum mechanical energy in the spring-block system

These two terms together represent the difference in total energy in the lab frame and the total energy in the moving frame.
I understand it now by backward reasoning ,since I know the expression for total energy in lab frame and moving frame . But what if I had approached with this method first .

How do we write total energy in the lab frame ?

Total energy in lab frame = Total energy in moving frame + ???

TSny
Homework Helper
Gold Member
From an earlier post you had ##E(t) = \frac{1}{2}m(v+v')^2 + \frac{1}{2}kx^2##. In another post, you have expressions for ##x## and ##v'## as functions of time. So, you should be able to get ##E(t)## as an explicit function of time. I was thinking that in post#13 you were giving an alternative way of approaching the problem . But now I realize that the edited part was an alternate/faster way to analyze the expression for the total energy .

Right ?

.

Last edited:
TSny
Homework Helper
Gold Member I was thinking that in post#13 you were giving an alternative way of approaching the problem . But now I realize that the edited part was an alternate/faster way to analyze the expression for the total energy .

Right ?
Yes. The first way was to get E(t) explicitly as a function of time. The second was to express E in terms of v and v' and get the answer by inspection.

• Vibhor
One last question , am I right in concluding that during the course of motion the work done by external agent pulling the free end would be both positive and negative ? Alternate positive and negative work would be done by the agent .

??

TSny
Homework Helper
Gold Member
One last question , am I right in concluding that during the course of motion the work done by external agent pulling the freed end would be both positive and negative ? Alternate positive and negative work would be done by the agent .

??
Yes, there are times when the pulling force is doing positive work and times when it is doing negative work. The total work done (starting at t = 0) varies between 0 and 2mv2 over and over again. So, the total work done since the start is never negative.

• Vibhor
Thank you very much Sir .