1.SECOND ORDER DIFFERENTIAL EQUATION Solve the equation d?x dx -2 + 2x 85 sin 3t dr? dt given that when t= 0, x = 0 and- = -20. Show that the values of %3D dt t for stationary values of the steady-state solution are the roots of 6 tan 31 = 7. A mass suspended from a spring performs vertical oscillations and the displacement x (cm) of the mass at time t (s) is given by d²x dr =4&x f x = and = 0 when t = 0, determine the period and amplitude of the oscillations. The equation of motion of a body performing damped forced vibra- d?x tions is- +5+ 6x = cos t. Solve this equation, given that x = 0-1 dx dt and = 0 when t = 0. Write the steady-state solution in the form K sin (t + a).
1.SECOND ORDER DIFFERENTIAL EQUATION Solve the equation d?x dx -2 + 2x 85 sin 3t dr? dt given that when t= 0, x = 0 and- = -20. Show that the values of %3D dt t for stationary values of the steady-state solution are the roots of 6 tan 31 = 7. A mass suspended from a spring performs vertical oscillations and the displacement x (cm) of the mass at time t (s) is given by d²x dr =4&x f x = and = 0 when t = 0, determine the period and amplitude of the oscillations. The equation of motion of a body performing damped forced vibra- d?x tions is- +5+ 6x = cos t. Solve this equation, given that x = 0-1 dx dt and = 0 when t = 0. Write the steady-state solution in the form K sin (t + a).
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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Transcribed Image Text:1.SECOND ORDER DIFFERENTIAL EQUATION
Solve the equation
d?x
dx
- 2
dt?
+ 2x = 85 sin 3t
dt
given that when t = 0, x = 0 and-
= -20. Show that the values of
%3D
dt
t for stationary values of the steady-state solution are the roots of
6 tan 3t = 7.
A mass suspended from a spring performs vertical oscillations and
the displacement x (cm) of the mass at time t (s) is given by
d²x
dr
=-48x
If x ={ and
dx
= 0 when t = 0, determine the period and amplitude
dt
of the oscillations.
The equation of motion of a body performing damped forced vibra-
d?x, dx
tions is+ 5 + 6x = cos t. Solve this equation, given that x = 0-1
dt
and
= 0 when t = 0. Write the steady-state solution in the form
K sin (t + a).
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