Bab 1 GHS
By : Vivi Fauzia
Bab 1 GHS
MEMAHAMI • Konsep Gerak H Harmonik ik S Sederhana d h • Hubungan GHS dengan gerak melingkar beraturan g dalam GHS • Energi • Aplikasi GHS dalam kehidupan sehari-hari
TARGET • Dapat menentukan ciri-ciri i i i i utama t GHS • Dapat menurunkan persamaan gerak dan energi pada berbagai kasus GHS • Dapat mencari aplikasi GHS dalam kehidupan sehari sehari-hari hari By : Vivi Fauzia
Bab 1 GHS
wire i θ
τ
m
I By : Vivi Fauzia
Bab 1 GHS
F = –kx
By : Vivi Fauzia
Bab 1 GHS
F = -kx k
• Hukum Newton :
a
F = ma = -kx =
m
x
w
2
d x Coba solusi x = A cos ωt atau x = A s sin ωt
Latihan 1
d 2x m 2 dt
PR 1
dt 2
k =− x m
d2x 2 = − ω x dt 2
Persamaa n differensia l x(t)
ω=
k m
By : Vivi Fauzia
PR 1 • • •
Turunkan persamaan gerak, solusi dan besar ω pada kasus gerak harmonik sederhana : Bandul sederhana Bandul puntir Massal pada tali teregang
Bab 1 GHS
x = A cos ω t + B sin ω t = a sin( ω t + φ ) dimana a =
A2 + B 2 Latihan 2
By : Vivi Fauzia
Bab 1 GHS
? x = a sin( ω t + φ ) dx = x = a ω cos( ω t + φ ) dt d 2x dt 2
= x = − a ω 2 sin( ω t + φ )
By : Vivi Fauzia
Diskusi
Bab 1 GHS
• Frekuensi radio Delta FM adalah 99 99,1 1 MHz apa artinya ? • Bagaimana cara melipatgandakan kecepatan maksimum GHS ?
By : Vivi Fauzia
Latihan soal •
Sebuah benda 2 kg dihubungkan dengan suatu pegas horisontal dengan konstata gaya s= 5 kN/m kN/m. Pegas diregangkan 10 cm dari titik kesetimbangan dan dilepas. Tentukan : a) b) c) d) e) f) g)
•
Frekuensi Perioda Amplitudo gerak Kecepatan maksimum Percepatan maksimum Kapan pertama kali benda mencapai kesetimbangan Percepatan saat mencapai kesetimbangan
Perioda partikel yang berosilasi adalah 8 s. Pada t=0, partikel berada pada x=A=10 cm. a) Sketsa posisi x sebagai fungsi dari waktu t b) Jarak yang ditempuh dalam detik pertama, kedua dan ketiga setelah t=0.
Bab 1 GHS
y 4
3
1
2 1
5 6
1
x0
-1
3 2
4 5 π 2 6
π
θ
By : Vivi Fauzia
Latihan soal •
Sebuah partikel bergerak pada lintasan lingkaran berjari-jari 15 cm, membuat 1 putaran setiap 3s 3s. Tentukan : – Laju partikel – Kecepatan sudut – Persamaan untuk komponen x posisi partikel sebagai fungsi waktu t dengan menganggap partikel berada pada sumbu x pada waktu t = 0. p
Bab 1 GHS
Latihan 3
Etotal = Epotensial & Ekinetik = konstan k = ½ kx2 + ½ ma2ω2 = ½ ka2
PR 2
U K E -A
0
U A
s
By : Vivi Fauzia
PR 2 •
Turunkan persamaan energi untuk 3 kasus (bandul sederhana, bandul puntir, tali teregang) dan gunakan persamaan dE =0 dt untuk memperoleh persamaan geraknya.
Latihan soal •
Sebuah benda 1 1,5 5 kg berGHS pada pegas yang mempunyai konstanta gaya ss= 500 N/m. N/m Laju maksimum 70 cm/s cm/s. Tentukan : – Energi total – Amplitudo osilasi
Bab 1 GHS
• Osilasi harmonik antara energi magnetik dan energi listrik Analogi g Mekanik - Listrik
2
dq q L 2 + =0 dt C Latihan 4
ω=
1 LC
F x m K
V q L C
By : Vivi Fauzia
Bab 1 GHS
Latihan 5 UB dan UE ? 1.2
Ratio o of U E to UB
1 08 0.8 0.6 0.4 0.2 0 0
02 0.2
04 0.4
06 0.6
08 0.8
1
12 1.2
-0.2 Time in Periods
By : Vivi Fauzia
Bab 1 GHS
microphone Quartz Clock
Atomic clock
By : Vivi Fauzia
Atomic Clock •
•
•
Scientists had long realized that atoms (and molecules) have resonances; each chemical element and compound absorbs g radiation at its and emits electromagnetic own characteristic frequencies. These resonances are inherently stable over time and space The cesium atom's natural frequency was f formally ll recognized i d as th the new international unit of time in 1967: the second was defined as exactly 9,192,631,770 oscillations or cycles of the cesium atom's atom s resonant frequency frequency, replacing the old second that was defined in terms of the Earth's motions. As of January, 2002, NIST's latest primary cesium standard was capable of keeping time to about 30 billionths of a second per year. Called NIST-F1, it is the 8th of a series of cesium clocks built by NIST and NIST's first to operate on the "fountain" principle. i i l
The world's smallest atomic clock •
•
•
about the size of a rice grain, is built around a microcell about 1 mm3 in volume filled with cesium atoms. It draws only about 30 mA of current from a 2.5 V battery. y Atomic clocks are the best timekeepers p because they y are able to convert the high-precision information contained in the light emitted by alkali atoms (the light emerging from an atomic transition from one energy level to another can be measured to an uncertainty of better than a part in a billion) into a usable standard for defining the second. Th new miniature The i i clock l kh has a precision i i off 3 3.5 x 10 10-10. 10 Wh What this hi means iis that events can be timed with an uncertainty of about one part in 3 billion. Scientists at NIST in Boulder, Colorado make atomic clocks that are far more precise---the F-1 clock is good to about one part in 10 trillion---but this requires a huge table-top’s table-top s worth of equipment. equipment The mini version being reported now should eventually reach a stability of about 10-11, some 10,000 times better than any quartz oscillator clock of equivalent size and power. How will this new cheap, tiny, low-power, low power, high high-precision precision MEMS clock be used? In satellites, GPS receivers, networked computer CPU’s, possibly in cell phones. (Knappe et al., Applied Physics Letters, 30 August 2004; contact John Kitching,
[email protected], 303-497-3328; for an explanation of precision and accuracy, see NIST Time & Frequency glossary.) l )
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