The Physics
Opus in profectus


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  1. A "seconds pendulum" has a half period of one second. It takes one second for it to go out (tick) and another second for it to come back (tock).
    1. What is the length of a seconds pendulum at a place where gravity equals the standard value of 9.80665 m/s2?
    2. What is the period of this same pendulum if it is moved to a location near the equator where gravity equals 9.78 m/s2? How much time does the pendulum lose or gain every 30 days?
    3. What is the period of this same pendulum if it is moved to a location near the north pole where gravity equals 9.83 m/s2? How much time does the pendulum lose or gain every 30 days?
  2. The Great Clock of Westminster
    The Great Clock of Westminster is undoubtedly the world's most famous clock. It is sometimes called "Big Ben", but strictly speaking that is the name of the 13.7 tonne Great Bell. The 12 × 12 × 96 meter tower that houses the Great Clock is the iconic symbol of the British Parliament. Many home doorbells and school bells are programmed to play the Westminster Quarters — the four permutations of four notes that announce the quarter hours. During World War II, the Great Clock was a symbol of British resiliency. It continued to operate even after sustaining damage in a German air raid in 1941. (The House of Commons chamber was destroyed in this attack.)
    1. The heart of the timekeeping mechanism is a 310 kg, 4.4 m long steel and zinc pendulum. What is the period of the Great Clock's pendulum? This is not a straightforward problem.
      1. Begin by calculating the period of a simple pendulum whose length is 4.4 m.
      2. The period you just calculated would not be appropriate for a clock of this stature. What is the most sensible value for the period of this pendulum?
      3. What is the cause of the discrepancy between your answers to parts i and ii?
    2. Pennies are used to regulate the clock mechanism (pre-decimal pennies with the head of Edward VII). Adding one penny causes the clock to gain two-fifths of a second in 24 hours. The pennies are not added to the pendulum bob (it's moving too fast for the pennies to stay on), but are instead placed on a small platform not far from the point of suspension.
      1. Read this quote from a 2007 article in the Daily Mail. "When the clock is found to be gaining or losing time, the weight of the pendulum is fractionally adjusted by the addition or removal of an old-fashioned penny piece." While this statement is true, it does not explain how adding a penny affects the operation of the pendulum. What error did the reporter make in his explanation?
      2. Why does this method really work; that is, what does adding pennies near the top of the pendulum change about the pendulum?
      3. Now for a mathematically difficult question. By what amount did the important characteristic of the pendulum change when a single penny was added near the pivot?
  3. Write something different.
  4. simple-pendulum.txt
    A classroom full of students performed a simple pendulum experiment. They attached a metal cube to a length of string and let it swing freely from a horizontal clamp. They recorded the length and the period for pendulums with ten convenient lengths. Use these results to determine the acceleration due to gravity at this location.


  1. An object swings from the end of a cord as a simple pendulum with period T. An identical object oscillates up and down on the end of a vertical spring with the same period T. If the masses of both objects are doubled, how will the new values of the periods (call them Tp and Ts) compare to T?
  2. trajectories-pendulum.pdf
    The drawings on the accompanying pdf worksheet show a pendulum as it swings from left to right. A pair of scissors is used to cut the string cleanly and instantly at four different positions. Sketch the subsequent trajectory of the mass until it lands on the ground.