Chapter 5, Problem 5.15P

In considering question #4, how fast is the mass moving when it is half way between the equilibrium and maximum amplitude, AND what is the kinetic and potential energies at that location?

In the case of a damped pendulum, how would the dyanmics change as a fixed point varied from being a stable spiral, to a stable degenerate node, to a stable node? I know that all the trajectories continue to lose altitude, and that the pendulum goes from whirling clockwise over the top, loses energy, settles to a small oscillation, and eventually comes to rest at the bottom, but wasn't sure if this general description changes based on the variation of fixed points.

Find and find the oscillation time of an oscillator with a harmonic of amplitude 0.4m passing through the origin with an initial velocity of 0.6m / s?

After a long space trip where you are in stasis, your autonomous ship lands you on a planet you don’t recognize. Having the equipment on board the ship to make a pendulum, you put one together with a bob of mass 25 g and a length of 50 cm. You find the period to be 1.4 s. Are you on earth? If not, is the planet you are on more or less massive than earth?

While visiting the Albert Michelson exhibit at Clark University, you notice that a chandelier (which looks remarkably like a simple pendulum) swings back and forth in the breeze once every T = 6.6 seconds. Frequency is = 1/6.6 Angular Velocity = 0.952 Length of the chandelier = 10.81 That evening, while hanging out in J.J Thompson's House O' Blues, you notice that (coincidentally) there is a chandelier identical in every way to the one at the Michelson exhibit except this one swings back and forth 0.11 seconds slower, so the period is T + 0.11 Seconds. Determine the acceleration due to gravity in m/s^2 at the club