00:03
Given that w equal to 14 lb and stretch s equal to 2 feet and acceleration due to gravity g equal to 32 feet 12 seconds square, we have to find damping constant beta.
00:32
The solution is the concept we are going to use here is like m is the mass and kbbd spring constant and beta beta be the damping constant according to newton's law m d squared by d2 square equal to minus d x minus beta multiplied by d x divided by dt x x x with the displacement from equilibrium position.
01:56
D square x divided by dt square plus beta divided by m multiplied by dx divided by dt plus k divided by m multiplied by x equal to zero.
02:11
Consider this equation first.
02:14
The marks m equal to w divided by g equal to 14 lb divided by 32 feet per second square equal to 7 divided by 16 slug from hook slough k equal to w divided by s equal to 10 l root divided by 2 fit equal to 5 lb divided by 5 putting values in equation first d square x divided by dt square plus 16 divided by 7 multiplied by beta multiplied by d x divided by d2 plus 5 multiplied by 16 divided by 7 multiplied by x equal to 0.
03:20
Now denoting the coefficient to lambda equal to 16 veta divided by 7, that implies that lambda equal to 8 divided by 7 beta and w square equal to k divided by 10 equal to 80 divided by 7.
03:57
Lambda square minus w square equal to 64 divided by 49, beta square minus 80 divided by 7.
04:08
In part, in, motion is over them, lambda square minus w square greater than 0, 64 divided by 49, multiplied by beta square minus 80, divided by 7 is greater than 0...