EF 158 - Spring 2006 – Exam 3 - Page 1 of 6
Name _____________________________________
1. The graph of displacement versus time
for a 14.3 g mass at the end of a spring
(i.e., a Simple Harmonic Oscillator SHO) is shown at right.
a) (10 pts) Write an equation for the
displacement x as a function of
time t.
b) (10 pts) For the SHO above, what is the spring constant k?
EF 158 - Spring 2006 – Exam 3 - Page 2 of 6
Name _____________________________________
2. a) (10 pts) At what displacement of a SHO is the total energy half kinetic and half potential? Express your
answer as a factor times the maximum displacement.
b)
(10 pts) What fraction of the total energy of a SHO is kinetic and what fraction is potential when the
displacement is half the amplitude?
EF 158 - Spring 2006 – Exam 3 - Page 3 of 6
Name _____________________________________
3. A 2.00-kg mass oscillates on the end of a spring with spring constant 12.0 N/m. Its amplitude of oscillation
decreases from 10.0 cm to 1.00 cm in 4.00 minutes.
a) (10 pts) What is the mean lifetime of this oscillator?
b) (10 pts) What is the angular frequency at which this oscillator will have its peak amplitude?
EF 158 - Spring 2006 – Exam 3 - Page 4 of 6
Name _____________________________________
4. A gondola is connected to the top of a hill by a steel cable of length 625 m and mass 975 kg. As the gondola
comes to the end of its run, it bumps into the side and sends a wave pulse along the cable. It is observed that
it takes 16.5 s for the pulse to return,
a) (10 pts) What is the speed of the pulse?
b) (10 pts) What is the tension in the cable?
EF 158 - Spring 2006 – Exam 3 - Page 5 of 6
Name _____________________________________
5) A pendulum consists of a 4.00 kg uniform slender rod of length
l = 1.25 m with a "bob" of mass m = 12.0 kg on the end.
a) (10 pts) What is the period of this pendulum?
b) (10 pts) What would be the percentage error if one used the formula for the simple pendulum to
calculate the period?
EF 158 - Spring 2006 – Exam 3 - Page 6 of 6
Name _____________________________________