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Unformatted text preview: f the two: 37.5 J. 3 11. A If you start with a pendulum (*), you can decrease
its frequency by
A) making its string longer
B) increasing its mass
C) starting it from a larger angle
D) all of these E) none of these Page 6 (*) (A) (B) (C) 12. The ﬁgure shows a 10 kg cart attached to a spring, and
oscillating back and forth. At t = 0 s the spring is maximally compressed (5 cm shorter than normal) and the cart
is stationary. At t = 1 s the spring is its equilibrium length,
and at t = 2 s the cart is once again stationary because the
spring is maximally extended (5 cm longer than normal).
3 (a) What is the frequency f of this oscillation?
5cm It oscillates once every four seconds, so f = 1
t=1s 3 (b) A At t = 2 s, the cart’s acceleration
A) points to the left
B) is zero
C) points to the right t=2s
5cm . . . in the same direction as the force
Do one of these two problems, or both for extra credit.
2 (c) What is the spring constant k of the spring? The spring constant is related to the frequency via
= ω = 2πf =⇒ k = m(2πf )2 = (10 kg)(2π (0.25 /s))2 = 24.7 N/m
2 (d) How fast is the cart moving at t = 1 s? The velocity of an oscillating object is v (t) = Aω cos(ωt + φ0 ) and has a maximum value
of Aω , which it obtains when the cart is at equilibrium (t = 1 s). The amplitude A of the
oscillation is 5 cm = 0.05 m, and so the speed of the cart at t = 1 s is
Aω = A(2πf ) = (0.05 m)(2π )(0.25 Hz) = 0.079 m/s 3 13. B
A) air In which material is the speed of sound faster?
B) water C) both the same Page 7 D The ﬁgure shows a standing wave on a string. How many antinodes
does it have?
A) 2 B) 3 C) 4 D) 5 E) 6 Displacement !y (m) 3 14. v = 8m/s Position x (m) 15. The ﬁgure shows a snapshot of a wave on a string,
moving at 8 m/s to the right. A) 0.5 m C 2 (b) A) 0.5 m E 2 (c) second?
A) 0.25 The amplitude A of this wave is
B) 1 m C) 2 m D) 5 m The wavelength λ of this wave is
B) 1 m C) 2 m D) 5 m v = 8m/s Position x (m) As this wave moves, how many crests will pass the right-hand bord...
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