A mechanics question for Trinity College Interview Test

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100708244
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consider a mass m at position x(t) on a rough horizontal table attached to the origin by a spring with constant k (restoring force -kx) and with a dry friction force f \begin{cases}f=F, & \text{if $\dot x \lt 0$}\\-F \le f \le F, & \text{if $\dot x =0$}\\f=-F,& \text{if $\dot x \gt 0$}\end{cases}

a). What is the range of x where the mass can rest?

b) Show that if the mass moves, the maximum excursion decreases by \frac{2F}{k} per half cycle.

c) Discuss the motion

Could someone please give a hint as how to show that the amplitude of oscillation decrease per half cycle?
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Krollo
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Easiest way is probably energy. Let me know if you need a further prod.

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100708244
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(Original post by Krollo)
Easiest way is probably energy. Let me know if you need a further prod.

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Thanks! I've solved it both using energy methods and differential equations. It is too slow to type it here as the differential methods cost a lot of space.

For those interested, see http://physics.stackexchange.com/que...s-a-half-cycle
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Krollo
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(Original post by 100708244)
Thanks! I've solved it both using energy methods and differential equations. It is too slow to type it here as the differential methods cost a lot of space.

For those interested, see http://physics.stackexchange.com/que...s-a-half-cycle
Ah, excellent. Are you planning to try for Trinity? :ahee:

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100708244
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(Original post by Krollo)
Ah, excellent. Are you planning to try for Trinity? :ahee:

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No, my ability is not comparable to BMO participants. But I will try for Cambridge.
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A5ko
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(Original post by 100708244)
No, my ability is not comparable to BMO participants. But I will try for Cambridge.
Did someone say BMO?

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Krollo
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(Original post by 100708244)
No, my ability is not comparable to BMO participants. But I will try for Cambridge.
Great to hear it. Will you be applying for 2016?

Don't worry about BMO, it's a very particular style of maths, you won't be disadvantaged one bit.


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