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Take a Swing at your ComputerHold your mouse hanging by its cord. But don't tell us where on the cord you're holding it. We'll tell you.... Here's how:
What Happens If You Swing Too Hard?Simply put, the bigger the swing, the more complicated the equations have to be to deal with it. If you're swinging too hard, the rate that the pendulum swings starts to depend on how hard it swings as well as the length. When that happens, the computer will conclude the pendulum is a lot longer than it really is. Try it and see! The swing rate - the "frequency" - doesn't depend on how hard you swing - the "amplitude" - as long as you don't swing it too hard. For little swings, when the mouse swings out twice as far, gravity pushes back twice as hard. The mouse acts like a "simple harmonic oscillator," the only thing physicists really understand. But if you swing too hard, all that stuff isn't accurate anymore. Swing out twice as far, and gravity pushes back less than twice as hard. That makes things complicated. Equations get hard to solve, and swings take longer to complete. So the computer thinks the mouse cord must be longer than it really is.
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We got your computer to time the swinging mouse. And then we used a really cool equation physicists have worked out that takes into account the Earth's gravity (which is what makes a pendulum swing) and the number pi. (Pi is a little more than 3. It shows up whenever something moves back and forth.) Here's the equation: And it means:
When you plug the numbers for pi and gravity into the equation, the distance in centimetres works out to 25 times the square of the time per swing. (In inches, it's 10 times the time per swing squared.) Try another look at that equation.If you increase the distance from your hand to the mouse, then the time per swing ought to increase as well. Try it! What do you think would happen if gravity on Earth were stronger? Would a pendulum swing faster or slower? (Take a look at the equation again, you can figure it out.) Watch out! The equation doesn't work very well if you swing your mouse too hard. What Happens If You Swing Too Hard?Simply put, the bigger the swing, the more complicated the equations have to be to deal with it. If you're swinging too hard, the rate that the pendulum swings starts to depend on how hard it swings as well as the length. When that happens, the computer will conclude the pendulum is a lot longer than it really is. Try it and see! The swing rate - the "frequency" - doesn't depend on how hard you swing - the "amplitude" - as long as you don't swing it too hard. For little swings, when the mouse swings out twice as far, gravity pushes back twice as hard. The mouse acts like a "simple harmonic oscillator," the only thing physicists really understand. But if you swing too hard, all that stuff isn't accurate anymore. Swing out twice as far, and gravity pushes back less than twice as hard. That makes things complicated. Equations get hard to solve, and swings take longer to complete. So the computer thinks the mouse cord must be longer than it really is. And it's tricky to figure out what measuring to "the middle of the mouse" means. What Part of the Mouse Should You Measure From?The equations for the swinging mouse assume that you measure from a point near the mouse's centre of mass. Here's how to find your mouse's centre of mass: 
(The rounded Apple mouse balances near the middle of the ball. Your mouse balance may vary.) |
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