Martha's Marvellous Munchies

The endless murmur of traffic passing on the nearby dual carriageway has been muted.  There are no vapour trails crossing the blue sky overhead, and the sound of birds singing seems clearer than ever before.  The world has suddenly become a much quieter place. It turns out that we can change our habits and cut carbon dioxide emissions - for reasons that no one would have wanted, and a human and economic cost that we don't yet know.  The EU may achieve a 9% decrease in emissions in 2020 due to the coronavirus lockdown, but the big question is what happens afterwards.  Will this be a blip, or the start of a downward trend? Meanwhile, this period of enforced inactivity has given us an opportunity to reflect on the changes we have made so far, and maybe given some of us time to make a few more.  I just thought I'd share a few of mine - not to show off, as a lot of people are way ahead of me, but to give us all a little more hope and inspiration to keep making our own smal

Yesterday I hooked some nuts onto an old paperclip, tied it to a piece of string, and hung the string from a windowsill outside my house.  When I lifted it to one side and let go, it swung, just as I knew it would, ticking smoothly and silently from side to side until it settled again in the vertical position.  I smiled with satisfaction. Credit: Wikimedia Commons The boys, of course, weren't anywhere near as enthusiastic when I suggested we could measure the length of time that the pendulum took to swing to and fro.  They managed a few half-hearted observations before running off to the trampoline again.  But my brain was starting to remember a few hazy physics facts, and I was intrigued.  Shortening the string obviously reduced the swing time, but by how much?  Could I figure out what the relationship was?  I shortened, measured, measured again, made a few calculations, drew a graph... ah yes!  Now I remembered what this was like... It's been quite a while since I