A force of 8 pounds stretches a spring 1 foot. A mass weighing 3.2 pounds is attached to the spring, and the system isthen immersed in a medium that offers a damping force numerically equal to 0.8 times the instantaneous velocity.(a) Find the equation of motion if the mass is initially released from rest from a point 1 foot above theequilibrium position.x(t)ft

Question
Asked Oct 4, 2019
109 views
A force of 8 pounds stretches a spring 1 foot. A mass weighing 3.2 pounds is attached to the spring, and the system is
then immersed in a medium that offers a damping force numerically equal to 0.8 times the instantaneous velocity.
(a) Find the equation of motion if the mass is initially released from rest from a point 1 foot above the
equilibrium position.
x(t)
ft
help_outline

Image Transcriptionclose

A force of 8 pounds stretches a spring 1 foot. A mass weighing 3.2 pounds is attached to the spring, and the system is then immersed in a medium that offers a damping force numerically equal to 0.8 times the instantaneous velocity. (a) Find the equation of motion if the mass is initially released from rest from a point 1 foot above the equilibrium position. x(t) ft

fullscreen
check_circle

Expert Answer

Step 1

Let m be the mass attached and k is the string constant and let β be the positive damping constant. The newton second law for the system is:

d x
,dx
т
dt
where x () is the displacement from equilibrium position
dt
therefore,
d x k
0
dr
т at
т
help_outline

Image Transcriptionclose

d x ,dx т dt where x () is the displacement from equilibrium position dt therefore, d x k 0 dr т at т

fullscreen
Step 2

Now, find the equation of motion. First, convert the weight into unit of masses:

3.2 lb
1
slug
32 ft/s2 10
help_outline

Image Transcriptionclose

3.2 lb 1 slug 32 ft/s2 10

fullscreen
Step 3

Now, find spring c...

W
k
8 lb
8lb/ft
1 foot
help_outline

Image Transcriptionclose

W k 8 lb 8lb/ft 1 foot

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Advanced Math