Which equation correctly describes the position, x, of the mass as the function of time, t? [let the frequency of the oscillation as fl

a) Find the surface gravity and escape velocity of a planet with a mass of (6.7× 1023 kg) and a radius of (2.9 × 106 m).b) What is the local acceleration due to gravity of a planet on which a pendulum of length (0.4 m) undergoes (5 oscillations) in (13 s)?c) If the planet from part (b) has a radius of (R = 5 × 106 m), what is the mass of the planet?

(Figure 1)A bob of mass mmm is suspended from a fixed point with a massless string of length LLL (i.e., it is a pendulum). You are to investigate the motion in which the string moves in a cone with half-angle θθtheta. How long does it take the bob to make one full revolution (one complete trip around the circle)? Express your answer in terms of some or all of the variables mmm, LLL, and θθtheta, as well as the free-fall acceleration ggg.

Consider the “Foucault pendulum”, as shown below. Foucault set up his 1851 spherical pendulum (of mass m and length L) experiment in the Pantheon dome of Paris, showing that the plane of oscillation rotates and takes about 1.3 days to fully revolve around. This demonstrated the extent to which Earth’s surface is not an inertial reference frame (e.g., role of the Coriolis force). Your task here is to determine (but not solve) the equations of motion.