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Key points OSCILLATIONS
 
 
 
Oscillations ,[object Object],[object Object],[object Object]
Oscillations ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Oscillations ,[object Object],[object Object],[object Object],[object Object]
t = 0 t = T/4 t = T/2 t = 3T/4 t = T
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
[object Object],Its motion is called  simple harmonic motion
Simple Harmonic Motion ,[object Object],[object Object],[object Object],[object Object]
Simple Harmonic Motion ,[object Object]
Simple Harmonic Motion
Simple Harmonic Motion ,[object Object],[object Object],Keeping  ω  &  Φ  constant varying  x m  …
Simple Harmonic Motion ,[object Object],[object Object],[object Object]
Simple Harmonic Motion ,[object Object],[object Object],[object Object]
The Velocity of SHM ,[object Object],[object Object]
The Velocity of SHM
The Velocity of SHM ,[object Object],[object Object]
The Acceleration of SHM ,[object Object]
The Acceleration of SHM ,[object Object]
The Acceleration of SHM ,[object Object],[object Object]
[object Object]
[object Object],[object Object]
[object Object],[object Object]
The Force Law for SHM ,[object Object],This force is called  restoring force k is called  force constant
The Force Law for SHM ,[object Object],[object Object],Where  ω  is  natural frequency
Simple Harmonic Oscillator ,[object Object]
 
Mass-spring system ,[object Object]
Problem 1 ,[object Object],[object Object],[object Object],[object Object],[object Object]
Problem 2 ,[object Object],[object Object]
Solution of problem 2
 
P 17.3 To be on the verge of slipping means that the force exerted on the smaller block is :-
P 17.5
Continued ……. P 17.6
 
P 17.7
P 17.7
E 17.17
Energy in SHM ,[object Object],[object Object]
Energy in SHM ,[object Object],[object Object]
Energy in SHM ,[object Object],Using the velocity function and also making a substitution of  ω 2   = k/m  we get:
Energy in SHM ,[object Object]
Energy in SHM So we finally get The  total energy  of a linear oscillator is  constant and independent of time
Energy in SHM ,[object Object],[object Object]
 
 
Energy Conservation in Oscillatory Motion
At any time t E = U (t) + K (t) = constant Differentiating w. r. t. t
Energy Law in SHM
Problem 3 ,[object Object],[object Object],[object Object]
[object Object],Solution problem 3 (b)  PE ( at x  =  - 2.0  cm)  =  PE ( at x  =  + 2.0  cm)  =  2J (c) PE ( x = - x m ) =  U max  =  E  =  5J
P 17.13
P 17. 8 Continued …. .
 

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