# Category Archives: M2 mechanics

# STEP I/1994/9

# Some STEP probability and mechanics questions

Some STEP probability and mechanics questions from Michael Gibson’s “mini-mock” papers. These questions can be done with relatively short working and without needing to use any great knowledge of formulas. Continue reading

# Maths prize 17 November 2017: ball and bucket

# Preparing for an M2 resit

# Answer to STEP III 2007 Q.11

Mechanics of a wheel falling off the edge of a table. Continue reading

# Answer to STEP III 2007 Q.9

III/2007/9 – Two small beads, A and B, each of mass *m*, are threaded on a smooth horizontal circular hoop of radius *a* and centre O. The angle θ is the acute angle determined by 2 θ = AOB.

The beads are connected by a light straight spring. The energy stored in the spring is

where *k* and α are constants satisfying *k* > 0 and

The spring is held in compression with θ = β and then released. Find the period of oscillations in the two cases that arise according to the value of θ and state the value of β for which oscillations do not occur. Continue reading