Coupled Pendulum - universe.bits-pilani.ac.in
Transcript of Coupled Pendulum - universe.bits-pilani.ac.in
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Coupled Pendulum
Aim
To study normal modes of oscillations of two coupled pendulums and to measure the frequncies of these normal modes, as well as the spring constant k.
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Coupled Pendulum
Apparatus
● Two compound pendulums● Coupling spring● Stop watch
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Coupled Pendulum
The Set-up
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Procedure (Part I)
● Uncouple the two pendulums (remove the spring) and bring the peg to which the spring is attached at the bottom.
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Procedure (Part I)
● Set small oscillations in both the pendulums individually and measure period T for 20 oscillations. Calculate natural frequency ω
0.
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Procedure (Part I)● The height l (10, 15, and 20 cm) of the peg to which spring is attached is measured from the mid point of the peg to the pivot.
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Procedure (Part I)
● Hook the spring at l=10 cm. Make sure the spring should neither slack nor stretch.
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Procedure (Part I)
● Displace both the pendulums SLIGHTLY in one direction by the same amount to excite the in-phase normal mode. Calculate T
1 and ω
1 for 20 oscillations.
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Procedure (Part I)● Now displace both the pendulums SLIGHTLY in opposite directions by the same amount to excite the out-of-phase normal mode. Calculate T
2 and ω
2 for
20 oscillations.
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Procedure (Part I)
● Repeat the procedure for l=15 cm and l=20 cm.
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Procedure (Part II)
● Set l=10 cm.
● Displace any one pendulum by a small amount.
● Measure T for a single (one) oscillation. (For this, measure T for 20 oscillations and
divide the number by 20.)
● Measure time period ΔT between two successive stops of the same pendulum. ● Using these T and ΔT, verify the frequencies, ω
1 and ω
2 , measured in part I.
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Calculations and Graphs
● Plot versus l2 and versus l2.
● From the slope of versus l2, calculate the spring constant of the coupling spring. Slope = 2k/mgL
ω22
ω02
ω12
ω02
ω22
ω02
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Coupled Pendulum