15.4 Pendulums  (Page 4/7)

Pendulum clocks are made to run at the correct rate by adjusting the pendulum’s length. Suppose you move from one city to another where the acceleration due to gravity is slightly greater, taking your pendulum clock with you, will you have to lengthen or shorten the pendulum to keep the correct time, other factors remaining constant? Explain your answer.

A pendulum clock works by measuring the period of a pendulum. In the springtime the clock runs with perfect time, but in the summer and winter the length of the pendulum changes. When most materials are heated, they expand. Does the clock run too fast or too slow in the summer? What about the winter?

With the use of a phase shift, the position of an object may be modeled as a cosine or sine function. If given the option, which function would you choose? Assuming that the phase shift is zero, what are the initial conditions of function; that is, the initial position, velocity, and acceleration, when using a sine function? How about when a cosine function is used?

What is the length of a pendulum that has a period of 0.500 s?

Some people think a pendulum with a period of 1.00 s can be driven with “mental energy” or psycho kinetically, because its period is the same as an average heartbeat. True or not, what is the length of such a pendulum?

What is the period of a 1.00-m-long pendulum?

How long does it take a child on a swing to complete one swing if her center of gravity is 4.00 m below the pivot?

The pendulum on a cuckoo clock is 5.00-cm long. What is its frequency?

Two parakeets sit on a swing with their combined CMs 10.0 cm below the pivot. At what frequency do they swing?

(a) A pendulum that has a period of 3.00000 s and that is located where the acceleration due to gravity is $9.79{\text{m/s}}^2$ is moved to a location where the acceleration due to gravity is $9.82{\text{m/s}}^2$ . What is its new period? (b) Explain why so many digits are needed in the value for the period, based on the relation between the period and the acceleration due to gravity.

A pendulum with a period of 2.00000 s in one location ( $g=9.80{\text{m/s}}^2$ ) is moved to a new location where the period is now 1.99796 s. What is the acceleration due to gravity at its new location?

(a) What is the effect on the period of a pendulum if you double its length? (b) What is the effect on the period of a pendulum if you decrease its length by 5.00%?