**Title: Understanding Pendulum Clocks and Gravity**You are visiting your grandparents in Boston. There is an antique grandfather clock keeping time in one of the rooms. Your grandmother enters the room and tells you that she had it calibrated professionally in Denver and it kept perfect time for years. After they moved it here to their Massachusetts house, it has not been accurate. It runs too fast and has to be reset to the correct time every few days. You find some papers associated with the calibration of the clock when it was in Denver and find the following. The pendulum of the clock consists of a long, thin rod of length \( L = 1.14 \, \text{m} \) and mass \( m = 0.450 \, \text{kg} \). On the rod is mounted a sliding bob, which is a uniform disk of radius \( R = 0.115 \, \text{m} \) and mass \( M = 2.10 \, \text{kg} \). The rod is suspended from pins mounted at its upper end. The calibration data show the acceleration due to gravity in Denver to be \( 9.796 \, \text{m/s}^2 \). You measure very carefully and find that the center of the disk is located at a distance \( r = 1.0140 \, \text{m} \) from the pivot point at the upper end of the rod.(a) **Find the period of the pendulum (in s) when it was in Denver.**[ ______ ] s(b) **The acceleration due to gravity in Boston is \( 9.803 \, \text{m/s}^2 \). If the Denver-calibrated clock is set to the correct time one morning in Boston, determine by how many seconds the clock is off at the same time the next morning.**[ ______ ] sIs it fast or slow?- [ ] fast- [ ] slow(c) **You decide to adjust the clock by turning a small knob located at the bottom of the bob. Turning the knob causes the bob to move up and down on the rod. Find the direction you should move the bob to restore the correct timekeeping capability of the clock: up or down.**[ ] up[ ] down**Explanation:**This problem explores the concepts of pendulum motion and how variations in gravitational acceleration can affect time **Problem Statement:**A toddler with a mass of 14.4 kg bounces up and down in her crib. The crib mattress behaves like a light spring with a force constant of 1840 N/m.**Questions:**(a) The toddler bounces with a frequency that allows her to reach a maximum amplitude with minimum effort. What is this frequency (in Hz)?[Answer Box] Hz(b) The toddler now bounces high enough to lose contact with the mattress once each cycle, like a trampoline. What is the minimum amplitude of oscillation (in cm) required for this to occur?[Answer Box] cm**Help Section:**Need Help? [Read It Button]

Note:As per our guidelines we are supposed to answer only one question. Kindly repost other questions as the seperate question. b)Fast Reason-Since the Period in Boston is shorter, So the Pendulum will make more swings in a day and run fasts c)Down Reason-Moving the Bob Downwards increases the effective length and lengthens the period