Objectives To determine if a standardised method of leg positioning without stirrups reduces the physical discomfort and sense of vulnerability and increases the sense of control among women undergoing speculum examination as part of a routine gynaecological examination. Design Randomised clinical trial. Setting Family medicine outpatient clinic. Patients 197 adult women undergoing routine gynaecological examination and cervical smear. Intervention Examination with or without stirrups. Main outcome measures Women's perceived levels of physical discomfort, sense of vulnerability, and sense of control during the examination, measured on 100 mm visual analogue scales. Results Women undergoing examination without stirrups had a reduction in mean sense of vulnerability from 23.6 to 13.1 (95% confidence interval of the difference − 16.6 to − 4.4). Mean physical discomfort was reduced from 30.4 to 17.2 ( − 19.7 to − 6.8). There was no significant reduction in sense of loss of control. Conclusion Women should be able to have gynaecological examinations without using stirrups to reduce the stress associated with speculum examinations.

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Theoretical problems involving equivalent resistances of large or infinite networks of resistors have received substantial attention. We consider two actual networks. In the first, the resistance is measured across one end of a ladder whose number of loops is incremented until the precision of the multimeter is exceeded. In the second, resistances are measured across nodes near the center of a 12 by 12 square grid of resistors. These experiments are useful in the introductory physics laboratory as interesting examples of equivalent resistance, and can be added to a standard Ohm’s law experiment. The square grid apparatus also can be employed for lecture demonstrations. In addition, this apparatus offers approximate experimental confirmation of complicated theoretical calculations for the equivalent resistance between two nonadjacent nodes of an infinite square grid. These experimental results are verified numerically.

One of the two normal modes of a system of two coupled nonlinear oscillators is subject to an instability. Several demonstration apparatus of weakly coupled oscillators that exhibit the instability are described. The effect is due to one normal mode parametrically driving the other, and occurs for the broad range of systems where the nonlinearity has a cubic contribution to the restoring force of each oscillator, which includes pendulums. The instability has an amplitude threshold that increases as the coupling is increased. A naive physical approach predicts that the mode opposite to that observed should be unstable. This is resolved by a weakly nonlinear analysis which reveals that the nonlinearity causes the linear frequency of a normal mode to depend upon the finite amplitude of the other mode. Numerical simulations confirm the theory, and extend the existence of the instability and the accuracy of the theoretical amplitude threshold beyond the regime of weak nonlinearity and weak coupling.

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