These selected solutions are intended for students who wish to know more of the background to selected, more difficult questions, or alternative methods to solutions posted elsewhere online. We also provide corrections to solutions posted online or to incomplete solutions. Our solutions are intended for students who want to know everything. These longer solutions are good candidates for Oxford interview questions. Contact us (use our online chat) if you would like more explanation of our solutions or of other past paper questions.

## Oxford PAT 2017 (Specimen), long solution notes

Download our Oxford PAT 2017 (Specimen) long solution notes. Take particular note of qu.25 where we give an expanded solution, explaining how the difference between dynamic and static friction comes into play in this question and why the tension remains lower than the frictional force in the dynamical region even though both jump downwards once sliding takes place. Note that questions 15 and 27 have technical errors in solutions posted online elsewhere which we correct here. In qu. 23 we explain why v=3u and in qu. 26 we provide an alternative solution to another online post where our solution is geometrical and uses less algebra.

## Oxford PAT 2016, long solution notes

Download our Oxford PAT 2016 long solution notes. We provide an expanded solution to qu. 16 to show explicitly how the plus and minus solutions contradict the assumption of the position of the -q charge, i.e. how the solutions are selected.

## Oxford PAT 2012, qu.22 long solution

Download our Oxford PAT 2012, qu. 22 solution. We provide a long solution as it is reasonably difficult. This question could just about be done in full in the time allowed, but to do so would be very challenging. But what if this is presented at interview - could you reproduce the argument in full? This question shows that even simple piecewise linear force functions F(x) are quite complex.

Note that the gradient of v(t) must equal a(t), which serves as a visual check. For a general solution of SHM see e.g. the formula sheet from Eduqas (WJEC).

See our tweet where we correct a well-known service provider's answers to this tricky Oxford PAT question, where problems in their solution are (noted in the tweet) as follows:

a3: t-intercepts for a(t) & v(t) not correct to 1 s.f. Doesn't discuss these graphs are periodic, i.e. repeat indefinitely.

b1: v(x) for x>0 not straight lines (see our graph). Doesn't discuss that the particle orbits indefinitely.

b2:Distance calculated is incorrect.

Note also that this provider does not expose that the motion is SUVAT for x>0 and SHM for x<0 where the particle is injected into the SHM region x<0 with a velocity to the left.

This post is incorrect in many details.

This other post is not completely right: e.g. their v(t) is not rotationally symmetric about the middle; a(t) not shown flat on the right!

b1: v for x>0 not straight lines (cf. our graph), no jumps in v versus x; only 1 cycle drawn.

b2: distance incorrect.

In our solution for the graph in b1, 15 orbits are drawn for clarity, but the particle cycles around indefinitely. Can you predict what happens as t tends to infinity?