Harmonic+Motion+2

Physics with Math -> **Harmonic Motion 2** Previous Next

Talking about simple harmonic motion ... media type="custom" key="9447544"

From this video you can see that there are many things to think about with simple harmonic motion.

**Questions:** The formula for T in the video works only for pendulums and is an approximation. We will //Hooke// a different formula for springs. Let's interact with a pendulum - Next
 * * What does T measure? What is the unit?
 * If T is bigger, what change would we see?
 * What was the formula for T in the video? What does it depend on?
 * Name some things that the formula does NOT depend on.
 * The length of the string on my pendulum is 4 times longer than the string on my friend's pendulum. Which T is bigger?
 * I want my pendulum to cycle faster (without changing string length). Should I go to Mars or Jupiter with my rocket? || [[image:rocket.gif]] ||

The unit is **seconds** because the unit m/s<² is used for the acceleration of gravity.
 * Answer:** T measures the cycle time, that is the time needed to complete a full swing and return to the point you were looking at when you started to measure.
 * Answer:** If T is bigger, the cycle time is longer. So the oscillation is slower, that is the frequency of oscillations is smaller.
 * Answer:** The formula for T is: [[image:http://latex.codecogs.com/gif.latex?%5Cinline%20T=2%5Cpi%5Csqrt%7B%5Cfrac%7B%5Cell%7D%7Bg%7D%7D]] It depends on ℓ and //g//.
 * Answer:** The formula for T does NOT depend on:
 * the time of day
 * the mass of the weight on the end of the string
 * how far out you pull the string before letting go
 * Answer:** T will be bigger on my pendulum. In fact it will be twice as big and move twice as slowly - why?
 * Answer:** To go faster, T needs to be smaller. This means g needs to be bigger (why?). So I need to go to a bigger planet than Earth to get more gravity. I will go to Jupiter.

If T₁ is the cycle time of a pendulum with string length ℓ₁ and T₂ with ℓ₂