Γ΄Λυκ-Κεφ2-Απλό (Μαθηματικό) Εκκρεμές

Απλό (ή Μαθηματικό) Εκκρεμές
Η [b]Απλή Αρμονική Ταλάντωση[/b] (ΑΑΤ) είναι η κίνηση στην οποία μία φυσική ποσότητα (λ.χ. η θέση, η γωνία θέσης, το φορτίο πυκνωτή, η ένσταση τού ρεύματος σε ένα κύκλωμα) είναι ημιτονοειδής συνάρτηση τού χρόνου, με συχνότητα ανεξάρτητη από το πλάτος τής ταλάντωσης. Έτσι, παραδείγματος χάρη, η κίνηση που εκτελεί σώμα συνδεδεμένο με ιδανικό ελατήριο που κινείται χωρίς τριβές εκτελεί ΑΑΤ, αφού η θέση του μεταβάλλεται ημιτονοειδώς με τον χρόνο.[br][br][br][b][size=85][size=150]Περιοδική κίνηση και ΑΑΤ:[/size][/size][br][/b][b][br]Περιοδικη κίνηση[/b] είναι κάθε κίνηση η οποία επαναλαμβάνεται η ίδια μετά από χαρακτηριστικό χρονικό διάστημα, την περίοδο. [br][br]Μία ιδιαίτερη περίπτωση περιοδικής κίνησης είναι η [b]ΑΑΤ[/b]. [u]Προϋπόθεση[/u] για ΑΑΤ είναι η συνισταμένη δύναμη που δέχεται ο ταλαντωτής να είναι γραμμική δύναμη επαναφοράς: να είναι αντίρροπη και ανάλογη τής μετατόπισης από τη θέση ισορροπίας (Θ.Ι). [center][br][math]F=-Dx[/math][/center]Επιπλέον, η Μηχανική Ενέργεια τού σύστηματος θα πρέπει να διατηρείται: Οι δυνάμεις που δρουν σ΄αυτό με μη μηδενικό έργο θα πρέπει να είναι διατηρητικές, να ορίζονται δηλ. από μια συνάρτηση δυναμικής ενέργειας. [br][center][math]F=-\frac{dU}{dx}[/math][/center][br]Ως εκ τούτου, εφόσον η δύναμη είναι γραμμική συνάρτηση τής θέσης, η αντίστοιχη δυναμική ενέργεια είναι δευτεροβάθμια συνάρτηση τής θέσης.[br][center][br][math]F=-\frac{dU}{dx}\Longrightarrow\int dU=-\int F_x\cdot dx\LongrightarrowΔU=-\int-Dx\cdot dx\LongrightarrowΔU=\frac{1}{2}Dx^2[/math][/center][img]data:image/png;base64,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[/img][br]
Στην περίπτωση τού απλού εκκρεμούς, σημειακή μάζα m αναρτάται από αβαρές και μη εκτατό νήμα μήκους L, όπως φαίνεται στο πιο κάτω σχήμα. Η κίνησή του είναι περιοδική, αλλά [b]δεν είναι αρμονική.[/b] Στο σώμα δρουν η δύναμη τής τάσης τού νήματος [math]\vec{F}_T[/math] και βαρυτική δύναμη [math]\vec{F}_G[/math]. Το διάνυσμα τής συνισταμένης δύναμης εκφρασμένο σε πολικές συντεταγμένες [math]\left(_r^{\wedge},_θ^{\wedge}\right)[/math]:[br][math]\sum\vec{F}=\vec{F}_T+\vec{F}_G=-mgsin\left(θ\right)_θ^{\wedge}[/math][br][br]Είναι φανερό ότι η συνισταμένη δύναμη είναι δύναμη επαναφοράς, εφόσον τείνει να επαναφέρει το σώμα στη θέση ισορροπίας [math]θ=0[/math], όμως δεν εξαρτάται γραμμικά από τη γωνιακή μετατόπιση [math]θ[/math]. Συνεπώς η κίνηση δεν είναι ΑΑΤ.[br][br]Ωστόσο, μπορούμε να προσεγγίσουμε την κίνηση ως ΑΑΤ για μικρές γωνίες εκτροπής από τη θέση ισορροπίας για τις οποίες [math]sin\left(θ\right)\congθ[/math] αποτελεί καλή προσέγγιση. Αυτό γίνεται εμφανές στο γράφημα τής δύναμης ως συνάρτησης τής γωνίας θέσης [math]θ[/math], όπου η ημιτονοειδής καμπύλη προσεγγίζεται πολύ καλά από την ευθεία [math]F=-mgθ[/math] για τιμές τού [math]θ[/math] πολύ κοντά στο [math]0[/math], δηλαδή για θέσεις κοντά στη Θ.Ι. Επίσης, στην προσέγγιση τής μικρής γωνίας η συνάρτηση τής δυναμικής ενέργειας [math]U\left(θ\right)[/math] προσεγγίζεται ικανοποιητικά από παραβολή, δηλαδή για τιμές του [math]θ[/math] κοντά στη Θ.Ι. η δυναμική ενέργεια είναι δευτεροβάθμια συνάρτηση τής γωνίας θέσης, [math]U\left(θ\right)\proptoθ^2[/math].[br][br][img]data:image/png;base64,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[/img][br][br]Πολλά συστήματα μπορούν να μοντελοποιηθούν ως Απλοί Αρμονικοί Ταλαντωτές, όπως η περίπτωση των μουσικών οργάνων (λ.χ. στοιχειώδη τμήματα χορδής έγχορδου ή στήλης αέρα πνευστού οργάνου) και η κίνηση διατομικού μορίου στην Κβαντική Φυσική. Σε αυτές και σε άλλες εφαρμογές είναι πιο χρήσιμο να θεωρούμε την ΑΑΤ υπό όρους ενέργειας, παρά δύναμης.
Fermer

Information: Γ΄Λυκ-Κεφ2-Απλό (Μαθηματικό) Εκκρεμές