Assume a bead of mass

m

slides along the curve

y = f ( x )

. Also assume that there is a damping force acting in the direction opposite to the velocity and proportional to the velocity, with proportionality constant

\beta

. The differential equation that describes the horizontal position of the bead is
A)

m \frac { d ^ { 2 } x } { d t ^ { 2 } } = - m g f ^ { \prime } ( x ) / \left( 1 - \left[ f ^ { \prime } ( x ) \right] ^ { 2 } \right) - \beta \frac { d x } { d t }

m \frac { d ^ { 2 } x } { d t ^ { 2 } } = - m g f ^ { \prime } ( x ) / \left( 1 - \left[ f ^ { \prime } ( x ) \right] ^ { 2 } \right) + \beta \frac { d x } { d t }

m \frac { d ^ { 2 } x } { d t ^ { 2 } } = - m g f ^ { \prime } ( x ) / \left( 1 + \left[ f ^ { \prime } ( x ) \right] ^ { 2 } \right) - \beta \frac { d x } { d t }

m \frac { d ^ { 2 } x } { d t ^ { 2 } } = m g f ^ { \prime } ( x ) / \left( 1 + \left[ f ^ { \prime } ( x ) \right] ^ { 2 } \right) - \beta \frac { d x } { d t }

m \frac { d ^ { 2 } x } { d t ^ { 2 } } = m g f ^ { \prime } ( x ) / \left( 1 + \left[ f ^ { \prime } ( x ) \right] ^ { 2 } \right) + \beta \frac { d x } { d t }

The Geometric Configuration of the Solutions Of dxdt=−6x−5y,dydt=4x+2y\frac { d x } { d t } = - 6 x - 5 y , \frac { d y } { d t } = 4 x + 2 ydtdx​=−6x−5y,dtdy​=4x+2y

Multiple Choice

Correct Answer:VerifiedUnlock this answer nowGet Access to more Verified Answers free of chargeAccess For Free

The Geometric Configuration of the Solutions Of $\frac { d x } { d t } = - 6 x - 5 y , \frac { d y } { d t } = 4 x + 2 y$

Correct Answer:
Verified
Unlock this answer now
Get Access to more Verified Answers free of charge