Mechanical Vibrations:
- Suppose that a mass weighing 16 lb stretches a spring 4 in. If the mass is displaced an additional 3 in and is
then set in motion, determine the position of the mass at any later time. Also determine the period, amplitude, and phase of the motion. solution
- Suppose that a mass weighing 10 lb stretches a spring 2 in. If
the mass is displaced an additional 2 in and is then set in motion with
an initial upward velocity of 1 ft per sec, determine the position of
the mass at any later time. Also determine the period, amplitude, and
phase shift of the motion. solution
- An object that weighs 16 lb stretches a spring 3 in. The object
is attached to a viscous fluid with a damping constant of 2 lb s per
feet. If the object is set in motion from its equilibrium position with
a downward velocity of 3 in per sec, find the position at any time t.
Determine when the mass first returns to its equilibrium position.
solution
- An object that weighs 8 lb stretches a spring 2 in. The object is attached to a viscous fluid with a damping constant of 2 lb sec per feet.
If the object is set in motion from its equilibrium position with a downward velocity of 2 in per sec,
find the position at any time t. Determine when the mass first returns to its equilibrium position. solution
- A 3 kg object is attached to spring and will stretch the spring
39.2 cm by itself. There is no damping in the system and a forcing
function of the form \( F(t) = 10 \cos (wt)\) is attached to the object
and the system will experience resonance. If the object is initially
displaced 20 cm downward from its equilibrium position and given a
velocity of 10 cm/sec upward find the displacement at any time t. solution