Simple harmonic motion of two pendulums

[Abhishekdas]

Homework Statement

Two pendulums of time periods 3s and 7 s respectively start oscillating simultaneously from two opposite extreme positions. After how much time they will be in the same phase?

Homework Equations

The Attempt at a Solution

Now what exactly is the question meaning by phase...In shm i only know of initial phase and phase difference...How can two pendulums with different time periods be in the same phase...Please help...

 

[zhermes]

Phase refers to the position of the pendulum in its oscillation. For instance, if a pendulum started oscillating from the left, we might say its phase was zero when it started, phase was pi when it reached the top of its path to the right, and 3*pi/2 when it reached the bottom of its swing on the way back.

The question is asking how long will it take for the motion of the two pendula to match up i.e. when will they be in the same relative position (and same motion of travel).

 

[Abhishekdas]

The question is asking how long will it take for the motion of the two pendula to match up i.e. when will they be in the same relative position (and same motion of travel).

hi zhermes... i did not exactly get wat you meant...do you mean to say when will they have the same position? But for that their initial pahses are required or rather their phase difference...

 

[zhermes]

do you mean to say when will they have the same position? But for that their initial pahses are required or rather their phase difference...

You do know their initial position (i.e. where they started).

I was trying (and failing) to also illustrate that there is a slight difference between position and phase.
1) position depends on how high the pendulum swings, where-as phase just depends on where in the cycle the pendulum is.
2) because phase is 'where in the cycle the pendulum is' it also depends on which direction the pendulum is moving. I.e. If the pendulum is at the lowest point (equilibrium position), it has a different phase if its traveling to the left than if its traveling to the right---even though the 'position' would be the same.

Does that make sense? (Sorry, I'm not doing my best explaining today)

 

[Abhishekdas]

haha...Firstly i am sorry i forgot that their initial positions are given ok...
still ...lets see...

now...ya...i got the two point where you mentioned the difference between position and pahse that ok...but...

ok...do you mean to say that when will they come to a position where their position in the cycle and direction is same? by position I mean their angular position... i don't what i mean by angular position though...i don't know what i am saying myself...I am no good either at explaining myself...

 

[Abhishekdas]

mathematecally do you mean the time when the angle traversed by onependulum+180(their initial phase diff) - angle traversed by the other pendulum in that time=intgram multiple of 360?

or else if we take the analogy of shm in a circle then they both are at the same position in the circle? is that what you mean?

 

[zhermes]

You have the right idea.
I think its better to think about the times and 'positions in the cycle' rather than angles.

Lets think of a simpler case: a 1sec pendulum ("1" starting @ left) and a 2s pend ("2" starting @ right).

After they are released, '1' will reach the right side, when '2' reaches the bottom. '1' will travel back to the left, when '2' reaches the left. At this point, both with be at the left, traveling to the right, and thus in the same phase. In this case, the answer would be 2 seconds.

 

[Abhishekdas]

Got it...i framed an equation such that the angle covered by one is 180 less than the other and got the answer...thanks...