damped harmanic oscillator, has damping aonstant a B = 2 Wo, that is acted upon bya driving force F Fo sin wt The System Starts from rest with an initial displacement of 10)=0), Find the equation of motian and itS corres panding solution x(t), determine all Of the coefficients (e.g. AL,A2, B, Bzretc) Xe li.e, xL0) = Xo and
damped harmanic oscillator, has damping aonstant a B = 2 Wo, that is acted upon bya driving force F Fo sin wt The System Starts from rest with an initial displacement of 10)=0), Find the equation of motian and itS corres panding solution x(t), determine all Of the coefficients (e.g. AL,A2, B, Bzretc) Xe li.e, xL0) = Xo and
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Question
Transcribed Image Text:damped harmanic oscillator, haS
damping constant
a
= 2 We, that is acted upon by a driving force
F
= Fo sin wt, The system Starts from rest With an
and
initial displacement of
Xo lie,xLO) = Xo
10)=0), Find the equation of motion and its
corres panding salution xlt), determine all of the
coefficients le.g., Ai,A2, B,, Bzretc)
%3D
Be,Bz,et c)
Expert Solution
Step 1
Given:
Driven force F = Fo sin
Damping Constant
Fid the equation of motion and its corresponding solution x(t)
Step 2
Driven Force F=Fo
Here, = Amplitude of force
= Angular frequency
Let restoring force be -cx and damping force -. Then the equation of motion for oscillator of mass 'm' can be expressed as
----- Equation (1)
Where, =2k ; = ;
In Steady-state the oscillator will execute oscillations of frequency . We get
Where A = Amplitude, = Phase angle
Differentiating equation (2), with respect to we have
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