Problem 5. [based on $3.7 #5] A mass of 20g stretches a spring 5cm. Suppose that the mass is also attached to a viscous damper with a damping constant of 400dyn-s/cm. If the masss is pulled down an additional 2cm and then released, (a) Model this situation as a 2nd order initial value problem. (b) Solve it to determine the position u(t) of the mass at any time t. (c) Plot u(t) as a function of time (labelling your graph as appropriate). (d) Determine the quasi-frequency, quasi-period, as well as the ratio between the quasi-period and the period of the corresponding undamped motion. (e) Find the time τ such that |u(t)| < 0.05cm for all t > . T

Problem 5. [based on $3.7 #5] A mass of 20g stretches a spring 5cm. Suppose that the mass is also attached to a viscous damper with a damping constant of 400dyn-s/cm. If the masss is pulled down an additional 2cm and then released, (a) Model this situation as a 2nd order initial value problem. (b) Solve it to determine the position u(t) of the mass at any time t. (c) Plot u(t) as a function of time (labelling your graph as appropriate). (d) Determine the quasi-frequency, quasi-period, as well as the ratio between the quasi-period and the period of the corresponding undamped motion. (e) Find the time τ such that |u(t)| < 0.05cm for all t > . T

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.7: Applications

Problem 18EQ

See similar textbooks