Lab 10: Simple Harmonic Motion, Pendulum Only 3 more to go!!  mg T length = l A B C mg T T -mgsin  -mgcos  The x-component of the weight is the force that is restoring the mass to equilibrium! This is analogous to F = -kx from last week’s lab.

Remember that,  is the angular frequency, and it tells us how many oscillations occur per second. For a pendulum system: where g, is the acceleration of gravity and l, is the length of the pendulum Another useful quantity is the period, T. The period tells us how long it takes to complete one oscillation, for a pendulum system: It turns out we can write the displacement as a function of time, t (same as last week): x = x MAX cos(  t) The velocity can be written as: V = -  x MAX sin(  t), The acceleration: a = -  2 x MAX cos(  t)

What are we doing today? 2 experiments. The first will allow us to finally answer the questions? “Does size matter….for a pendulum?” The second experiment we will increase the length of the pendulum and measure the period. Then we will plot T 2 vs L