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M3 Dynamics/elastics question Watch

1. Question is attached. It's driving me nuts, I can't understand what is going on at all. After being released from C, the particle starts moving with SHM, with the centre of oscillation at the midpoint of AB. It says the amplitude is 0.4m, but I would have thought that C would be the 'extreme' point of the oscillation, i.e. the particle hits C and turns back around, making the amplitude 0.5m.

Also, a general question - I have no idea how to work out where the centre of oscillation is. When it's just one spring, I know it's where the spring is at its natural length, but when a particle is attached to two springs which are stretched out, I'm baffled. Does the point where each spring is at its natural length have any significance at all?
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2. (Original post by bzzz)
Question is attached. It's driving me nuts, I can't understand what is going on at all. After being released from C, the particle starts moving with SHM, with the centre of oscillation at the midpoint of AB. It says the amplitude is 0.4m, but I would have thought that C would be the 'extreme' point of the oscillation, i.e. the particle hits C and turns back around, making the amplitude 0.5m.
Book is wrong IMHO. Amplitude is 0.5, as that is the distance between the release point (where the velocity is zero) and the centre of oscillation (the midpoint of AB)

Also, a general question - I have no idea how to work out where the centre of oscillation is. When it's just one spring, I know it's where the spring is at its natural length, but when a particle is attached to two springs which are stretched out, I'm baffled. Does the point where each spring is at its natural length have any significance at all?
The centre of oscillation is where the net force acting on the particle is zero. Here it is the midpoint of AB, since the two springs are identical, and at the midpoint they have the same extension so exert equal and opposite forces, and hence the net force is zero, hence it is the centre of oscillation.
3. (Original post by ghostwalker)
Book is wrong IMHO. Amplitude is 0.5, as that is the distance between the release point (where the velocity is zero) and the centre of oscillation (the midpoint of AB)

The centre of oscillation is where the net force acting on the particle is zero. Here it is the midpoint of AB, since the two springs are identical, and at the midpoint they have the same extension so exert equal and opposite forces, and hence the net force is zero, hence it is the centre of oscillation.
Excellent, noted, thanks

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Updated: December 19, 2010
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