# Homework Help: Spring+Pendulum combined system

1. Dec 14, 2013

### SpaceExplorer

A weight W is suspended from a rigid support by a hard spring with stiffness constant 'K'. The spring is allowed to have only vertical motion. A simple pendulum of length 'l' with a bob of mass 'm' (mg<<W) is suspended from the weight W and is set oscillating in a horizontal direction. After sometime, the spring is observed to be exhibiting vertical oscillations of high amplitude. Are the 'Spring system' and 'Pendulum system' oscillating with the same frequency? And what should be the function 'f', if K=f(W,l)?

2. Dec 14, 2013

### Simon Bridge

That's a neat problem - have you had a go tackling it yet?
Have you, say, drawn free body diagrams for the two masses?

What is the context the problem is set?

I'm picturing a slinky coil attached to a piston-head (W) which moves up and down in a cylinder in the ceiling.
The end of the piston sticks out of a hole in the cylinder and there is a hook on the end.
The pendulum swings from the hook.
That about right?

3. Dec 14, 2013

### SpaceExplorer

I've tried. But there's so much approximation I needed to use to derive the final relation, (using energy consideration), I'm no longer satisfied with or sure about my answer. So better I thought if it be run by experts. I found both systems to be oscillating with the same freq. and K=w/l.
Yes, your physical description seems right.

4. Dec 15, 2013

### Simon Bridge

OK. You need a way to be confident in your solution (or to tell if you've made a mistake)?
Does it make sense that the two parts should have the same frequency in this situation?
Hint: resonance

5. Dec 15, 2013

### SpaceExplorer

Yes! That should be it, the question did say about the 'high amplitude' of the resultant oscillations, so there's a high possibility that the composite system is showing resonance, i.e the driven system may undergo oscillations at the same frequency as that of the driving system. Thanks for the help. It was great relearning resonance in the context of this problem.

6. Dec 15, 2013

### Simon Bridge

When you see coupled oscillators and "big amplitude" think of "resonance" and "normal modes".
Since there is no external driving force, the two oscillators will exchange energy periodically.

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