HW15 Handout Name: ___________________
1. A spring-mass system has a period of 2.1 s. At t = 0 it is at rest at x = -15 cm. Its equili
ium position is x = 0.
a. Give symbolic equations for the position, velocity, and acceleration as functions of time. .
. Find the maximum speed of the mass? At what t does this occur?
2.A spring with a force constant of 70 N/mis hung from the ceiling. A block of mass 0.27 kg is hung from it and set in
simple harmonic motion with an amplitude of 8 cm. What is the maximum speed of the mass? Watch your units!
HW15 Handout Name: ___________________
3. An horizontal spring-mass system on a frictionless surface consists of an 0.4 kg and a spring with constant 60 N/m. The
mass has a speed of 0.70 m/s when it is located 5 cm from the unstrained length.
a. What is the total mechanical energy of this system? Hint: 5 cm is not the amplitude!
. What is the greatest speed attained by the block during its oscillation?
4. A non-uniform picture frame with a mass of 3 kg is suspended from a nail located 10 cm from its center of mass.
When it oscillates at a small amplitude (as a physical pendulum), one complete cycle takes 2.6 s. Find the moment of
inertia of the picture frame about the nail.
HW15 Handout Name: ___________________
5. A spring-mass oscillator is made with an 0.4 kg mass. The spring has a damping constant of 0.01 kg/s. The oscillator
completes a cycle every 2.5 s.
a. By approximately what percentage does its mechanical energy decrease in each cycle? Show work!
a) 4%
) 5%
c) 6%
d) 7%
e) 8%
. Assuming the same mass and period, what damping constant would result in a 10% loss of energy per cycle?