Question
Asked Oct 31, 2019
Two 1.3 kg masses and three identical springs having a k value of 85 N/m are connected. What are the frequencies of the two longitudinal vibration
modes? The two periods?
 
f=1/2π √(k/m)
check_circleExpert Solution
Step 1

Draw the following diagram representing the 2 masses and 3 spring systems.

K
K
K
2
help_outline

Image Transcriptionclose

K K K 2

fullscreen
Step 2

Write the expression for the force on both the blocks.

F k(x-x) k(x,)
= m, (x-21)
F k(xx)- kx
.(1)
(2)
mt, =-k(2x2 -x)
k
1-2k
-2kx
k
help_outline

Image Transcriptionclose

F k(x-x) k(x,) = m, (x-21) F k(xx)- kx .(1) (2) mt, =-k(2x2 -x) k 1-2k -2kx k

fullscreen
Step 3

Write the expression for the kinetic and potential ...

1
1
2
2
1
k(x, -x,)*
2
U lk(x, )(x, - x)+ kx,x*
=(2x,-xxk(2x,-x)]
help_outline

Image Transcriptionclose

1 1 2 2 1 k(x, -x,)* 2 U lk(x, )(x, - x)+ kx,x* =(2x,-xxk(2x,-x)]

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

Science

Physics

Related Physics Q&A

Find answers to questions asked by student like you

Show more Q&A add