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## oscillations

### 1. Series 22. Year - 1. sliding and oscillations

Two weights of masses $m$ and $M$ are connected by a spring of stiffness $k$ and lies on flat smooth surface (friction can be neglected). Body of mass $m$ gets velocity $\textbf{v}$ (see picture). What will be the smallest distance between the bodies? And when it will be reached?

V ročenkách kanadské FO našel Honza Prachař.

### 1. Series 22. Year - 3. do not cradle me

Kathy is on a swing (a plank suspended on 2 ropes). At high displacements she kneels down, in lowest point she gets up. This movements she periodically repeats. Ration of distance of centre of gravity from the rotation axis at kneeling down and at standing is 2^{1 ⁄ 12} ≈ 1,06. How many times Kathy must swing to double the amplitude of swinging?

Z asijské olympiády přinesl Honza Prachař

### 3. Series 20. Year - 1. sandwiched flying saucer

The food on a transatlantic ship is prepared by a chef Thomas. He has very userful spring-based device to hold plates. The holder holds the top plate always in the same height regardless the number of plates in holder. The distance between plates is 1 cm. The weather is stormy and the plates are oscillating. What is the frequency of the oscillations?

### 4. Series 18. Year - P. vibrating glass

Having a small thin-wall glass and circling with the wetted finger on its edge very loud sound can be produced. When the water is poured into the glass, the pitch (frequency) of the sound is decreasing with increasing water level. Try this experimentally and explain this effect.

Robin

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