Download MATH 2800 Problem Set #9 1. A 24- pound weight is attached to the

MATH 2800 Problem Set #9
1.
A 24- pound weight is attached to the end of a spring and stretches it 4 ft.
Find the equation of motion and the amplitude and frequency of the
oscillations if the weight is released
a) from rest from a point 3 feet above equilibrium.
b) from an equilibrium position with an initial downward velocity of 2ft/s.
2.
An 8-pound weight attached to a spring stretches it 8/9 ft. The weight is
submerged in a viscous fluid that offers a resistance numerically equal to 
(with  > 0) times the instantaneous velocity. Determine the values of the
damping constant  so that the subsequent motion is: a) overdamped, b)
critically damped, c) damped. If the system starts at equilibrium with an
initial downward velocity of 9 ft/s, find the equation of motion, and make a
rough sketch of the graph for =15/4, =3, and = 5 .
3.
A 16-pound weight stretches a spring 8/3 ft. Initially, the weight starts from
rest 2 ft below equilibrium position, andthe subsequent motion takes place
in a medium that offers a damping force numerically equal to ½ the
instantaneous velocity. Find the equation of motion if the weight is driven
by an external force equal to :
a) cos(3t)
b) e-tcos(3t)
and describe the amplitude and frequency of the system after a very long
time.
4.
A mass of 1 slug is attached to a spring with constant 4 lb/ft. Write the
equation of motion and discuss the motion as time goes on if there is no
b) cos( 19
c) cos(2t)
damping, and an external force of a) cos t
10 t)
is applied.
