P Physics Multiple Choice Practice Oscillations. ass, attached to a horizontal assless spring with spring constant, is set into siple haronic otion. Its axiu displaceent fro its equilibriu position is. What is the ass s speed as it passes through its equilibriu position? ( ) 0 ( B) ( C) ( D). he period of a spring-ass syste undergoing siple haronic otion is. If the aplitude of the springass syste s otion is doubled, the period will be: () ¼ (B) ½ (C) (D) (E) 4 3. siple pendulu of ass and length L has a period of oscillation at angular aplitude θ = 5 easured fro its equilibriu position. If the aplitude is changed to 0 and everything else reains constant, the new period of the pendulu would be approxiately. () (B) ( ) (C) (D) / ( ) (E) / 4. ass is attached to a spring with a spring constant. If the ass is set into siple haronic otion by a displaceent d fro its equilibriu position, what would be the speed, v, of the ass when it returns to the equilibriu position? ( E) d d d ( ) v ( B) v ( C) v ( D) v gd ( E) g 5. ass on the end of a spring oscillates with the displaceent vs. tie graph shown. Which of the following stateents about its otion is INCORREC? () he aplitude of the oscillation is 0.08. (B) he frequency of oscillation is 0.5 Hz. (C) he ass achieves a axiu in speed at sec. (D) he period of oscillation is sec. (E) he ass experiences a axiu in the size of the acceleration at t=.5 sec v d 6. What is the period of a siple pendulu if the cord length is 67 c and the pendulu bob has a ass of.4 g. () 0.59 s (B).63 s (C) 3.86 s (D) 6.3 s (E) 4.3 s 7. If the ass of a siple pendulu is doubled but its length reains constant, its period is ultiplied by a factor of () (B) (C) (D) (E) 8. Which of the following is true for a syste consisting of a ass oscillating on the end of an ideal spring? () he inetic and potential energies are equal to each other at all ties. (B) he inetic and potential energies are both constant. (C) he axiu potential energy is achieved when the ass passes through its equilibriu position. (D) he axiu inetic energy and axiu potential energy are equal, but occur at different ties. (E) he axiu inetic energy occurs at axiu displaceent of the ass fro its equilibriu position 9. he length of a siple pendulu with a period on Earth of one second is ost nearly () 0. (B) 0.5 (C) 0.50 (D).0 (E) 0.0
Questions 0-: bloc oscillates without friction on the end of a spring as shown above. he iniu and axiu lengths of the spring as it oscillates are, respectively, x in and x ax. he graphs below can represent quantities associated with the oscillation as functions of the length x of the spring. 0. Which graph can represent the total echanical energy of the bloc-spring syste as a function of x? () (B) B (C) C (D) D (E) E. Which graph can represent the inetic energy of the bloc as a function of x? () (B) B (C) C (D) D (E) E. n object swings on the end of a cord as a siple pendulu with period. nother object oscillates up and down on the end of a vertical spring also with period. If the asses of both objects are doubled, what are the new values for the Periods? Pendulu Mass on Spring () (B) (C) (D) (E)
3. n object is attached to a spring and oscillates with aplitude and period, as represented on the graph. he nature of the velocity v and acceleration a of the object at tie /4 is best represented by which of the following? () v > 0, a > 0 (B) v > 0, a < 0 (C) v > 0, a = 0 (D) v = 0, a < 0 (E) v = 0, a = 0 4. When an object oscillating in siple haronic otion is at its axiu displaceent fro the equilibriu position. Which of the following is true of the values of its speed and the agnitude of the restoring force? Speed Restoring Force () Zero Maxiu (B) Zero Zero (C) ½ axiu ½ axiu (D) Maxiu ½ axiu (E) Maxiu Zero 5. particle oscillates up and down in siple haronic otion. Its height y as a function of tie t is shown in the diagra. t what tie t does the particle achieve its axiu positive acceleration? () s (B) s (C) 3 s (D) 4 s (E) None of the above, because the acceleration is constant 6. he graph shown represents the potential energy U as a function of displaceent x for an object on the end of a spring oscillating in siple haronic otion with aplitude x. Which of the following graphs represents the inetic energy K of the object as a function of displaceent x?
Questions 7-8 sphere of ass, which is attached to a spring, is displaced downward fro its equilibriu position as shown above left and released fro rest. sphere of ass, which is suspended fro a string of length L, is displaced to the right as shown above right and released fro rest so that it swings as a siple pendulu with sall aplitude. ssue that both spheres undergo siple haronic otion 7. Which of the following is true for both spheres? () he axiu inetic energy is attained as the sphere passes through its equilibriu position (B) he axiu inetic energy is attained as the sphere reaches its point of release. (C) he iniu gravitational potential energy is attained as the sphere passes through its equilibriu position. (D) he axiu gravitational potential energy is attained when the sphere reaches its point of release. (E) he axiu total energy is attained only as the sphere passes through its equilibriu position. 8. If both spheres have the sae period of oscillation, which of the following is an expression for the spring constant () L / g (B) g / L (C) L / g (D) g / L (E) g / L 9. bloc attached to the lower end of a vertical spring oscillates up and down. If the spring obeys Hooe's law, the period of oscillation depends on which of the following? I. Mass of the bloc II. plitude of the oscillation III. Force constant of the spring () I only (B) II only (C) III only (D) I and II (E) I and III
0. siple pendulu and a ass hanging on a spring both have a period of s when set into sall oscillatory otion on Earth. hey are taen to Planet X, which has the sae diaeter as Earth but twice the ass. Which of the following stateents is true about the periods of the two objects on Planet X copared to their periods on Earth? () Both are shorter. (B) Both are the sae. (C) Both are longer. (D) he period of the ass on the spring is shorter; that of the pendulu is the sae. (E) he period of the pendulu is shorter; that of the ass on the spring is the sae. siple pendulu of length l, whose bob has ass, oscillates with a period. If the bob is replaced by one of ass 4, the period of oscillation is () 4 (B) (C) (D) (E)4 Questions -3 0.l -ilogra bloc is attached to an initially unstretched spring of force constant = 40 newtons per eter as shown above. he bloc is released fro rest at tie t = 0.. What is the aplitude, in eters, of the resulting siple haronic otion of the bloc? () (B) (C) (D) (E) 40 0 4 3. What will the resulting period of oscillation be? () 40 s (B) 0 s (C) 0 s (D) 5 s (E) 4 s 4. ball is dropped fro a height of 0 eters onto a hard surface so that the collision at the surface ay be assued elastic. Under such conditions the otion of the ball is () siple haronic with a period of about.4 s (B) siple haronic with a period of about.8 s (C) siple haronic with an aplitude of 5 (D) periodic with a period of about.8 s but not siple haronic (E) otion with constant oentu
Questions 5-6 refer to the graph below of the displaceent x versus tie t for a particle in siple haronic otion. 5. Which of the following graphs shows the inetic energy K of the particle as a function of tie t for one cycle of otion? 6. Which of the following graphs shows the inetic energy K of the particle as a function of its displaceent x?
7. ass is attached to a vertical spring stretching it distance d. hen, the ass is set oscillating on a spring with an aplitude of, the period of oscillation is proportional to g () d g (B) g d (C) d g (D) d 8. wo objects of equal ass hang fro independent springs of unequal spring constant and oscillate up and down. he spring of greater spring constant ust have the () saller aplitude of oscillation (B) larger aplitude of oscillation (C) shorter period of oscillation (D) longer period of oscillation (E) lower frequency of oscillation (E) g Questions 9-30. bloc on a horizontal frictionless plane is attached to a spring, as shown above. he bloc oscillates along the x-axis with siple haronic otion of aplitude. 9. Which of the following stateents about the bloc is correct? () t x = 0, its velocity is zero. (B) t x = 0, its acceleration is at a axiu. (C) t x =, its displaceent is at a axiu. (D) t x =, its velocity is at a axiu. (E) t x =, its acceleration is zero. 30. Which of the following stateents about energy is correct? () he potential energy of the spring is at a iniu at x = 0. (B) he potential energy of the spring is at a iniu at x =. (C) he inetic energy of the bloc is at a iniu at x =0. (D) he inetic energy of the bloc is at a axiu at x =. (E) he inetic energy of the bloc is always equal to the potential energy of the spring. 3. siple pendulu consists of a l.0-ilogra brass bob on a string about.0 eter long. It has a period of.0 seconds. he pendulu would have a period of.0 second if the () string were replaced by one about 0.5 eter long (B) string were replaced by one about.0 eters long (C) bob were replaced by a 0.5-g brass sphere (D) bob were replaced by a 4.0-g brass sphere (E) aplitude of the otion were increased 3. pendulu with a period of s on Earth, where the acceleration due to gravity is g, is taen to another planet, where its period is s. he acceleration due to gravity on the other planet is ost nearly () g/4 (B) g/ (C) g (D) g (E) 4g 33. frictionless pendulu of length 3 swings with an aplitude of 0. t its axiu displaceent, the potential energy of the pendulu is 0 J. What is the inetic energy of the pendulu when its potential energy is 5 J? () 3.3 J (B) 5 J (C) 6.7 J (D) 0 J (E) 5 J
34. n ideal assless spring is fixed to the wall at one end, as shown above. bloc of ass M attached to the other end of the spring oscillates with aplitude on a frictionless, horizontal surface. he axiu speed of the bloc is v. he force constant of the spring is Mg Mgv Mv Mv Mv () (B) (C) (D) (E) 35. siple pendulu has a period of s for sall aplitude oscillations. he length of the pendulu is ost nearly () /6 (B) /4 (C) / (D) (E) 36. ass M suspended by a spring with force constant has a period when set into oscillation on Earth. Its period on Mars, whose ass is about /9 and radius / that of Earth, is ost nearly () /3 (B) /3 (C) (D) 3/ (E) 3 37. ass M suspended on a string of length L has a period when set into oscillation on Earth. Its period on Mars, whose ass is about /9 and radius / that of Earth, is ost nearly () /3 (B) /3 (C) (D) 3/ (E) 3 38..0 g ass is attached to the end of a vertical ideal spring with a force constant of 400 N/. he ass is set in siple haronic otion with an aplitude of 0 c. he speed of the.0 g ass at the equilibriu position is () /s (B) 4 /s (C) 0 /s (D) 40 /s (E) 00 /s 39. n object of ass hanging fro a spring of spring constant oscillates with a certain frequency. What is the length of a siple pendulu that has the sae frequency of oscillation? () / g (B) g / (C) g / (D) / g (E) g / 40. platfor of ass g is supported by a spring of negligible ass as shown. he platfor oscillates with a period of 3 s when the platfor is pushed down and released. What ust be the ass of a bloc that when placed on the platfor doubles the period of oscillation to 6 s? () g (B) g (C) 4 g (D) 6 g (E) 8 g