This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Math 251H Second Midterm Exam 75 minutes March 25, 2009 SAMPLE EXAM. 1 1. A 3 kg mass is suspended from a spring, which stretches the spring 5 m from its natural length. The system is placed into the liquid with damping constant 14 Newtonseconds per meter. At t = 0, the system is at rest at its equilibrium position, then receives an external force of 6cos( t ) Netwons. Assume is positive and g = 10 m/s 2 . (a) Set up an initial value problem that describes the motion of the mass. Be sure to explain any variables that appear in your equation. (b) For which value of will the system have resonance? (c) Find the steadystate solution. Solution: m= 3. From the equilibrium condition mg = KL , we have, K = 6. In addition, = 14. Therefore, the equation of motion is given by, 3 u + 14 u + 6 u = 6cos t,u (0) = 0 ,u (0) = 0 . The natural frequency is radicalbig K/m = 2. Resonance occurs when the frequency is close to the natural frequency....
View
Full
Document
This note was uploaded on 07/16/2011 for the course MATH 251 taught by Professor Chezhongyuan during the Spring '08 term at Pennsylvania State University, University Park.
 Spring '08
 CHEZHONGYUAN
 Math, Differential Equations, Equations, Partial Differential Equations

Click to edit the document details