Conversation started Apr 26, 2023 at 5:02.
Wolgwang
Wolgwang
Apr 26, 2023 05:02
@JohnRennie Hi! Free?
John Rennie
John Rennie
Hi, yes I'm free.
Wolgwang
Wolgwang
Why the maximum compression occurs after 3/4(time period) ?
When two blocks are connected by a spring
user image
John Rennie
John Rennie
The way to understand questions like this is that in the centre of mass frame the motion is just simple harmonic.
The motion of the blocks is a combination of the two blocks executing SHM about the centre of mass, and the centre of mass moving at a constant velocity.
Dies this make sense so far?
Wolgwang
Wolgwang
Yes
John Rennie
John Rennie
In this case the COM is moving at 5 m/s to the right. Yes?
Wolgwang
Wolgwang
Apr 26, 2023 05:12
Yes
John Rennie
John Rennie
user image
So in the COM frame the motion looks like this.
At time zero the spring is at its relaxed length (whatever that is) so T/4 later it is at its maximum extension.
T/2 later it has expanded then returned to its relaxed length
And 3T/4 it is at maximum compression.
Then at T it has completed one cycle and it's back at its relaxed length.
Does this make sense?
Wolgwang
Wolgwang
@JohnRennie Why?
John Rennie
John Rennie
The questions says with the spring undeformed. Yes?
Wolgwang
Wolgwang
Yes
John Rennie
John Rennie
i.e. the spring starts out at its relaxed length i.e. unstretched.
Wolgwang
Wolgwang
Apr 26, 2023 05:22
@JohnRennie Time period T implies that if it started undeformed at t=0, then it will again be undeformed at t=T , right?
So at t=T/2 shouldn't it have max extension?
John Rennie
John Rennie
The oscillation looks like this:
- the mass start moving outwards at time zero
- they reach maximum extension at time T/4 and they start moving inwards again
- they get back to the centre at 2T/4, now they are moving inwards
- they reach maximum compression at 3T/4, then they start moving outwards again
- they get back to the centre again at 4T/4
So the spring is undeformed twice per cycle.
Wolgwang
Wolgwang
Ah got it!
John Rennie
John Rennie
OK :-)
 
Conversation ended Apr 26, 2023 at 5:28.