1. Undamped Forced Oscillations

2. External Forcing SHO with an additional external force
Why this particular type of force ?
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3. For any arbitrary time varying force
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4. Driving force:
Where

5. Equation of motion
x=xr+ixi

6. 2nd order linear homogeneous differential equation
with constant coefficients
General solution :
x1 (t) and x2 (t) are linearly independent,
i.e x1 (t) NOT proportional to (t) x2

7. 2nd order linear inhomogeneous differential equation
with constant coefficients
General solution :
Complementary function
Particular integral: obtained by special methods, solves the equation
with f(t)0; without any additional parameters
A & B : obtained from initial conditions

8. Obtaining the particular integral
Trial solution
Therefore
Hence

9. Amplitude, Relative Phase
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10. At resonance [w = w0, for wt=p/2,3p/2…]

11. Amplitude and Phase

12. Low Frequency Response
Stiffness Controlled Regime

13. High Frequency Response
Mass Controlled Regime

14. Summary Undamped forced oscillation (from PI)
Stiffness controlled regime (w<w0)
Resonance (w=w0)
Mass controlled regime (w>w0)

15. References FEYNMAN LECTURES ON PHYSICS VOL I
Author : RICHARD P FEYNMAN,
IIT KGP Central Library