lecture 4- simple harmonic motion chapter 15.1-15jn511/lectures/lecture4slides.pdfadmin oscillations...

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Lecture 4- Simple Harmonic MotionChapter 15.1-15.3

Prof. Noronha-HostlerPHY-124H HONORS ANALYTICAL PHYSICS IB

Phys- 124HFeb. 9th, 2018

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Tutoring

Tutoring for a fee:http://physics.rutgers.edu/descr/tutorpage2017.pdfMath and Science Learning Center:https://rlc.rutgers.edu/services/peer-tutoring

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Test

No notes. Equations will be providedSimple calculators allowed (NO phones, scientificcalculators etc).No. 2 pencils.No talking, no helping. Ask a proctor.Some questions might refer to the same figure.Don’t panic and carry a calculator.

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Combining waves

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Combining waves

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15.2.1. Object A is attached to ideal spring A and is moving in simple harmonic motion. Object B is attached to ideal spring B and is moving in simple harmonic motion. The period and the amplitude of object B are both two times the corresponding values for object A. How do the maximum speeds of the two objects compare?

a) The maximum speed of A is one fourth that of object B.

b) The maximum speed of A is one half that of object B.

c) The maximum speed of A is the same as that of object B.

d) The maximum speed of A is two times that of object B.

e) The maximum speed of A is four times that of object B.

15.2.1. Object A is attached to ideal spring A and is moving in simple harmonic motion. Object B is attached to ideal spring B and is moving in simple harmonic motion. The period and the amplitude of object B are both two times the corresponding values for object A. How do the maximum speeds of the two objects compare?

a) The maximum speed of A is one fourth that of object B.

b) The maximum speed of A is one half that of object B.

c) The maximum speed of A is the same as that of object B.

d) The maximum speed of A is two times that of object B.

e) The maximum speed of A is four times that of object B.

15.2.2. A steel ball is hung from a vertical ideal spring where it oscillates in simple harmonic motion with an amplitude of 0.157 m and an angular frequency of rad/s. Which one of the following expressions represents the acceleration, in m/s2, of the ball as a function of time?

a) a = 1.55 cos(t)

b) a = 1.55 cos2(t)

c) a = 0.157 cos(t)

d) a = 0.493 cos2(t)

e) a = 0.493 cos(t)

15.2.2. A steel ball is hung from a vertical ideal spring where it oscillates in simple harmonic motion with an amplitude of 0.157 m and an angular frequency of rad/s. Which one of the following expressions represents the acceleration, in m/s2, of the ball as a function of time?

a) a = 1.55 cos(t)

b) a = 1.55 cos2(t)

c) a = 0.157 cos(t)

d) a = 0.493 cos2(t)

e) a = 0.493 cos(t)

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Combining waves

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15.3.2. A spring is hung vertically from a fixed support. When an object of mass m is attached to the end of the spring, it stretches by a distance y. When an object of mass of 2m is hung from the spring, it stretches by a distance 2y. A second, identical spring is then attached to the free end of the first spring. If the object of mass 2m is attached to the bottom of the second spring, how far will the bottom of the second spring move downward from its unstretched position? Assume the masses of the springs are negligible when compared to m.

a) y/2

b) y

c) 3y/2

d) 2y

e) 4y

15.3.2. A spring is hung vertically from a fixed support. When an object of mass m is attached to the end of the spring, it stretches by a distance y. When an object of mass of 2m is hung from the spring, it stretches by a distance 2y. A second, identical spring is then attached to the free end of the first spring. If the object of mass 2m is attached to the bottom of the second spring, how far will the bottom of the second spring move downward from its unstretched position? Assume the masses of the springs are negligible when compared to m.

a) y/2

b) y

c) 3y/2

d) 2y

e) 4y

15.3.3. A spring is hung vertically from a fixed support. When an object of mass m is attached to the end of the spring, it stretches by a distance y. When an object of mass of 2m is hung from the spring, it stretches by a distance 2y. A second, identical spring is then attached to the fixed support as shown and a light rod is placed across the free ends of the springs. If the object of mass 2m is attached to the middle of the rod, how far will the rod move downward? Assume the masses of the springs and the rod are negligible when compared to m.

a) y/2

b) y

c) 3y/2

d) 2y

e) 4y

15.3.3. A spring is hung vertically from a fixed support. When an object of mass m is attached to the end of the spring, it stretches by a distance y. When an object of mass of 2m is hung from the spring, it stretches by a distance 2y. A second, identical spring is then attached to the fixed support as shown and a light rod is placed across the free ends of the springs. If the object of mass 2m is attached to the middle of the rod, how far will the rod move downward? Assume the masses of the springs and the rod are negligible when compared to m.

a) y/2

b) y

c) 3y/2

d) 2y

e) 4y

15.4.1. An ideal spring is hung vertically from a fixed support. When an object of mass m is attached to the end of the spring, it stretches by a distance y. The object is then lifted and held to a height y +A, where A << y. Which one of the following statements concerning the total potential energy of the object is true?

a) The total potential energy will be equal to zero joules.

b) The total potential energy will decrease and be equal to the gravitational potential energy of the object.

c) The total potential energy will decrease and be equal to the elastic potential energy of the spring.

d) The total potential energy will decrease and be equal to the sum of elastic potential energy of the spring and the gravitational potential energy of the object.

e) The total potential energy will increase and be equal to the sum of elastic potential energy of the spring and the gravitational potential energy of the object.

15.4.1. An ideal spring is hung vertically from a fixed support. When an object of mass m is attached to the end of the spring, it stretches by a distance y. The object is then lifted and held to a height y +A, where A << y. Which one of the following statements concerning the total potential energy of the object is true?

a) The total potential energy will be equal to zero joules.

b) The total potential energy will decrease and be equal to the gravitational potential energy of the object.

c) The total potential energy will decrease and be equal to the elastic potential energy of the spring.

d) The total potential energy will decrease and be equal to the sum of elastic potential energy of the spring and the gravitational potential energy of the object.

e) The total potential energy will increase and be equal to the sum of elastic potential energy of the spring and the gravitational potential energy of the object.

15.3.5. An ideal spring is hung vertically from a device that displays the force exerted on it. A heavy object is then hung from the spring and the display on the device reads W, the weight of the spring plus the weight of the object, as both sit at rest. The object is then pulled downward a small distance and released. The object then moves in simple harmonic motion. What is the behavior of the display on the device as the object moves?

a) The force remains constant while the object oscillates.

b) The force varies between W and +W while the object oscillates.

c) The force varies between a value near zero newtons and W while the object oscillates.

d) The force varies between a value near zero newtons and 2W while the object oscillates.

e) The force varies between W and 2W while the object oscillates.

15.3.5. An ideal spring is hung vertically from a device that displays the force exerted on it. A heavy object is then hung from the spring and the display on the device reads W, the weight of the spring plus the weight of the object, as both sit at rest. The object is then pulled downward a small distance and released. The object then moves in simple harmonic motion. What is the behavior of the display on the device as the object moves?

a) The force remains constant while the object oscillates.

b) The force varies between W and +W while the object oscillates.

c) The force varies between a value near zero newtons and W while the object oscillates.

d) The force varies between a value near zero newtons and 2W while the object oscillates.

e) The force varies between W and 2W while the object oscillates.