Answered

Discover the answers you need at Westonci.ca, where experts provide clear and concise information on various topics. Connect with a community of experts ready to provide precise solutions to your questions quickly and accurately. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

A 16 lb weight stretches a spring 6 inches in equilibrium. It is attached to a damping mechanism with constant c. Find all values of c such that the free vibration of the weight has infinitely many oscillations.

Sagot :

Manetho

Answer:

[tex]-8<c<8[/tex]

Explanation:

Given data:

Weight W = 16 lb

length l = 6/12 = 0.5 ft

hence, spring constant  k = W/l = 16/0.5 = 32 lb/ft

The equation of motion of spring is

[tex]mx''+cx+kx=0\\0.5x''+cx'+32x=0[/tex]

the auxiliary equation can be written as

[tex]0.5r^2+cr+32=0\\r^2+2cr+64=0[/tex]

The discriminate of equation is

[tex]D =(2c)^2+-4(1)(64)\\=4(c^2-64)[/tex]

To get the value of the damping constant,

[tex]D<0\\4(c^2-64)<0\\c>-8, c<8\\-8<c<8[/tex]

We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.