In an architectural installation, a spherical brass ornament is suspended from the ceiling by a light, inextensible cable so that it can swing freely as a pendulum. The measured distance from the pivot to the center of mass of the ornament is 0.95 m. Visitors set it in motion with an initial release angle of less than 4°, keeping the motion within the small-angle regime. Assume standard Earth surface conditions.
(a) Calculate the time required for one complete oscillation of the ornament. Show all steps and include appropriate units.
(b) Determine the oscillation frequency.
(c) The designers consider increasing the cable length by 0.20 m while keeping all other conditions unchanged. Calculate the new period and discuss how this change would affect visitors’ perception of the motion.
(d) Explain qualitatively whether increasing the initial release angle to 15° (while keeping the original 0.95 m length) would significantly alter the period. Justify your answer with physical reasoning rather than detailed calculation.