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What is the optimum speed of walking person to put a bridge into a maximum amplitude? Define parameters needed and then solve.

You can buy a roller on which surface a small bumps are located. The bumps then hit an edge of steel wafer, which have different length. In a song recorded on the roller you can find all tones in some interval (say, C major scale). Can you find out the shape of the wafers?

Marek made himself before Christmas a new toy: onto a wooden circle he put two nails (both nails and centre of circle in one line) and on two springs of stiffness $k$ he placed a weight of mass $m$. The weight can slide without friction on the surface of the wooden circle. Marek placed the circle onto a table and spin it around its axis with angular velocity $ω$, while the weight was slightly moved off the centre (equilibrium). Describe the movement of the weight, and as a bonus you can calculate it.

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?

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?

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?

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.