Pendulum Clocks will create a ticking sound every time the pendulum reaches maximum displacement on either side. It is desired to design a grandfather clock which will tick once every side. It is desired to design a grandfather clock which will tick once every second. The clock will stand 2.00 meters tall and it will be 32.0cm wide (interior width) all the way up and down. Suppose we can utilize a simple pendulum by a length of L and a point mass of M at the end.
a) By summing the torque around the suspension point, show that if we restrict the pendulum's motion to small angles, this will lead to simple harmonic motion. Do this for the general case, not this particular clock
b) Now using the data found in part a), decide the length of the pendulum that will give the desired period.
c) Given these dimensions, what is the percent error in making the small angle assumption? Suppose the pendulum swings during the maximum angle allowed with the clock's case. Use your calculators in RADIAN mode. In other words, compare θ to sin(θ)