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6.2. SECOND ORDER LINEAR ORDINARY DIFFERENTIAL EQUATIONS (ODE) (1) The ODE d2x dx +s- dt2 + kt = 0 m dt describes a damped, free oscillation of a mass m suspended on a spring, with c a positive damping constant and k the spring constant. The initial conditions are: dx x(0) = 0.16 and *(0) = 0 dt Assume for the mass = 10 kg and k = 90 and solve the equation for the following three damping constants (a)s = 100 kg/sec and (b) s = 0 to t = 10 sec. 10 kg/sec. Finally, plot all the cases in one graph from t =

6.2. SECOND ORDER LINEAR ORDINARY DIFFERENTIAL EQUATIONS (ODE) (1) The ODE d2x dx +s- dt2 + kt = 0 m dt describes a damped, free oscillation of a mass m suspended on a spring, with c a positive damping constant and k the spring constant. The initial conditions are: dx x(0) = 0.16 and *(0) = 0 dt Assume for the mass = 10 kg and k = 90 and solve the equation for the following three damping constants (a)s = 100 kg/sec and (b) s = 0 to t = 10 sec. 10 kg/sec. Finally, plot all the cases in one graph from t =

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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6.2. SECOND ORDER LINEAR ORDINARY DIFFERENTIAL EQUATIONS (ODE) (1) The ODE d²x dx + s dt2 m + kt = 0 dt describes a damped, free oscillation of a mass m suspended on a spring, with c a positive damping constant and k the spring constant. The initial conditions are: dx x(0) = 0.16 and = x(0) = 0 dt Assume for the mass = 10 kg and k = 90 and solve the equation for the following three damping constants (a) s = 100 kg/sec and (b) s = 10 kg/sec. Finally, plot all the cases in one graph from t = 0 to t = 10 sec.
Transcribed Image Text:6.2. SECOND ORDER LINEAR ORDINARY DIFFERENTIAL EQUATIONS (ODE) (1) The ODE d²x dx + s dt2 m + kt = 0 dt describes a damped, free oscillation of a mass m suspended on a spring, with c a positive damping constant and k the spring constant. The initial conditions are: dx x(0) = 0.16 and = x(0) = 0 dt Assume for the mass = 10 kg and k = 90 and solve the equation for the following three damping constants (a) s = 100 kg/sec and (b) s = 10 kg/sec. Finally, plot all the cases in one graph from t = 0 to t = 10 sec.
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