Differential Equations and Motion Analysis

This video tutorial explains the process of solving a damped force motion problem using differential equations. It begins with setting up the equation based on given initial conditions and external forces. The tutorial then walks through finding both the complementary and particular solutions, and concludes by determining the constants using initial conditions to arrive at the final solution. The video also includes a graphical representation of the motion.

What is the initial velocity of the mass in the upward direction?

• 1.5 meters per second

• 1 meter per second

• 2 meters per second

• 0.5 meters per second

What is the spring constant in the given problem?

• 100 Newtons per meter

• 120 Newtons per meter

• 140 Newtons per meter

• 160 Newtons per meter

Which term in the differential equation represents air resistance?

• C x prime

• Big F of T

• KX

• MX double prime

What is the value of the air resistance constant C?

• 80

• 95

• 85

• 90

What are the roots of the characteristic equation?

• Negative three and negative eight

• Negative four and negative nine

• Negative one and negative six

• Negative two and negative seven

What is the form of the complementary solution?

• C1 e^(-4t) + C2 e^(-9t)

• C1 e^(-2t) + C2 e^(-7t)

• C1 e^(-3t) + C2 e^(-8t)

• C1 e^(-t) + C2 e^(-2t)

What is the particular solution for the given problem?

• 13/500 cosine t + 9/500 sine t

• 15/500 cosine t + 10/500 sine t

• 12/500 cosine t + 8/500 sine t

• 14/500 cosine t + 11/500 sine t

What is the general solution of the motion?

• C1 e^(-t) + C2 e^(-2t) + 13/500 cosine t + 9/500 sine t

• C1 e^(-2t) + C2 e^(-7t) + 13/500 cosine t + 9/500 sine t

• C1 e^(-3t) + C2 e^(-8t) + 13/500 cosine t + 9/500 sine t

• C1 e^(-4t) + C2 e^(-9t) + 13/500 cosine t + 9/500 sine t

What is the value of C1 after solving the system of equations?

• -6/25

• -5/25

• -7/25

• -8/25

What is the value of C2 after solving the system of equations?

• 108/500

• 106/500

• 107/500

• 105/500