IB Questionbank Physics 1

1. The graph shows how the displacement varies with time for an object undergoing simple harmonic motion.

Which graph shows how the objects acceleration a varies with time t?

(Total 1 mark)

IB Questionbank Physics 2

2. A particle oscillates with simple harmonic motion with period T.

At time t = 0, the particle has its maximum displacement. Which graph shows the variation with time t of the kinetic energy Ek of the particle?

(Total 1 mark)

IB Questionbank Physics 3

3. The graph shows how the velocity v of an object undergoing simple harmonic motion varies with time t for one complete period of oscillation.

Which of the following sketch graphs best shows how the total energy E of the object varies with t?

(Total 1 mark)

IB Questionbank Physics 4

4. The graphs show how the acceleration a of four different particles varies with their displacement x. Which of the particles is executing simple harmonic motion?

(Total 1 mark)

IB Questionbank Physics 5

5. An object at the end of a spring oscillates vertically with simple harmonic motion. The graph shows the variation with time t of the displacement x. The amplitude is x0 and the period of oscillation is T.

Which of the following is the correct expression for the displacement x?

A. tT

x 2cos0

B. tT

x 2cos0

C. tT

x 2sin0

D. tT

x 2sin0

(Total 1 mark)

IB Questionbank Physics 6

6. Which of the following graphs shows the variation with displacement x of the speed v of a particle performing simple harmonic motion.

(Total 1 mark)

IB Questionbank Physics 7

7. Which graph correctly shows how the acceleration, a of a particle undergoing SHM varies with its displacement, x from its equilibrium position?

(Total 1 mark)

IB Questionbank Physics 8

8. A mass on the end of a horizontal spring is displaced from its equilibrium position by a distance A and released. Its subsequent oscillations have total energy E and time period T.

An identical mass is attached to an identical spring. The maximum displacement is 2A. Assuming this spring obeys Hookes law, which of the following gives the correct time period and total energy?

New time period New energy

A. T 4E

B. T 2E

C. T2 4E

D. T2 2E

(Total 1 mark)

9. A cart, connected to two identical springs, is oscillating with simple harmonic motion between two points X and Y that are equidistant from point O.

The cart is in equilibrium at

A. all points between X and Y.

B. point O only.

C. points X and Y only.

D. points O, X and Y only. (Total 1 mark)

IB Questionbank Physics 9

10. The graph below shows how the displacement x of a particle undergoing simple harmonic motion varies with time t. The motion is undamped.

Which of the following graphs shows how the total energy E of the particle varies with time t?

(Total 1 mark)

IB Questionbank Physics 10

11. The graph below shows the variation with time t of the displacement x of a particle undergoing simple harmonic motion.

Which graph correctly shows the variation with time t of the acceleration a of the particle?

(Total 1 mark)

12. Simple harmonic motion and the greenhouse effect

(a) A body is displaced from equilibrium. State the two conditions necessary for the body to execute simple harmonic motion.

1. .........................................................................................................................

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2. .........................................................................................................................

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IB Questionbank Physics 11

(b) In a simple model of a methane molecule, a hydrogen atom and the carbon atom can be regarded as two masses attached by a spring. A hydrogen atom is much less massive than the carbon atom such that any displacement of the carbon atom may be ignored.

The graph below shows the variation with time t of the displacement x from its equilibrium position of a hydrogen atom in a molecule of methane.

The mass of hydrogen atom is 1.7 1027 kg. Use data from the graph above

(i) to determine its amplitude of oscillation.

......................................................................................................................... (1)

(ii) to show that the frequency of its oscillation is 9.1 1013 Hz.

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IB Questionbank Physics 12

(iii) to show that the maximum kinetic energy of the hydrogen atom is 6.2 1018 J.

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(c) On the grid below, sketch a graph to show the variation with time t of the velocity v of the hydrogen atom for one period of oscillation starting at t = 0. (There is no need to add values to the velocity axis.)

(3)

(d) Assuming that the motion of the hydrogen atom is simple harmonic, its frequency of oscillation f is given by the expression

,21

pmkf

=

where k is the force per unit displacement between a hydrogen atom and the carbon atom and mp is the mass of a proton.

(i) Show that the value of k is approximately 560 N m1.

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IB Questionbank Physics 13

(ii) Estimate, using your answer to (d)(i), the maximum acceleration of the hydrogen atom.

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(e) Methane is classified as a greenhouse gas.

(i) Describe what is meant by a greenhouse gas.

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(ii) Electromagnetic radiation of frequency 9.1 1013 Hz is in the infrared region of the electromagnetic spectrum. Suggest, based on the information given in (b)(ii), why methane is classified as a greenhouse gas.

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(Total 17 marks)

IB Questionbank Physics 14

13. This question is about a simple pendulum.

(a) A pendulum consists of a bob suspended by a light inextensible string from a rigid support. The pendulum bob is moved to one side and then released. The sketch graph shows how the displacement of the pendulum bob undergoing simple harmonic motion varies with time over one time period.

On the sketch graph above,

(i) label with the letter A a point at which the acceleration of the pendulum bob is a maximum.

(1)

(ii) label with the letter V a point at which the speed of the pendulum bob is a maximum.

(1)

(b) Explain why the magnitude of the tension in the string at the midpoint of the oscillation is greater than the weight of the pendulum bob.

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IB Questionbank Physics 15

(c) The pendulum bob is moved to one side until its centre is 25 mm above its rest position and then released.

(i) Show that the speed of the pendulum bob at the midpoint of the oscillation is 0.70 m s1.

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(ii) The mass of the pendulum bob is 0.057 kg. The centre of the pendulum bob is 0.80 m below the support. Calculate the magnitude of the tension in the string when the pendulum bob is vertically below the point of suspension.

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IB Questionbank Physics 16

(d) The point of suspension of the pendulum bob is moved from side to side with a small amplitude and at a variable driving frequency f.

For each value of the driving frequency a steady constant amplitude A is reached. The oscillations of the pendulum bob are lightly damped.

(i) On the axes below, sketch a graph to show the variation of A with f.

(2)

(ii) Explain, with reference to the graph in (d)(i), what is meant by resonance.

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IB Questionbank Physics 17

(e) The pendulum bob is now immersed in water and the variable frequency driving force in (d) is again applied. Suggest the effect this immersion of the pendulum bob will have on the shape of your graph in (d)(i).

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(Total 16 marks)

14. This question is about simple harmonic motion.

(a) In terms of the acceleration, state two conditions necessary for a system to perform simple harmonic motion.

1. ..................................................................................................................................

2. .................................................................................................................................. (2)

(b) A tuning fork is sounded and it is assumed that each tip vibrates with simple harmonic motion.

The extreme positions of the oscillating tip of one fork are separated by a distance d.

(i) State, in terms of d, the amplitude of vibration.

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........................................................................................................................... (1)

IB Questionbank Physics 18

(ii) On the axes below, sketch a graph to show how the displacement of one tip of the tuning fork varies with time.

(1)

(iii) On your graph, label the time period T and the amplitude a. (2)

(c) The frequency of oscillation of the tips is 440 Hz and the amplitude of oscillation of each tip is 1.2 mm. Determine the maximum

(i) linear speed of a tip.

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(ii) acceleration of a tip.

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(Total 10 marks)

IB Questionbank Physics 19

15. This question is about simple harmonic motion and waves.

An object is vibrating in air. The variation with displacement x of the acceleration a of the object is shown below.

IB Questionbank Physics 20

(a) State and explain two reasons why the graph opposite indicates that the object is executing simple harmonic motion.

1. ..................................................................................................................................

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2. ..................................................................................................................................

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...................................................................................................................................... (4)

(b) Use data from the graph to show that the frequency of oscillation is 350 Hz.

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(c) The motion of the object gives rise to a longitudinal progressive (travelling) sound wave.

(i) State what is meant by a longitudinal progressive wave.

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IB Questionbank Physics 21

(ii) The speed of the wave is 330 m s1. Using the answer in (b), calculate the wavelength of the wave.

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(Total 12 marks)

16. This question is about oscillations and waves.

(a) A rectangular piece of wood of length l floats in water with its axis vertical as shown in diagram 1.

The length of wood below the surface is d. The wood is pushed vertically downwards a distance A such that a length of wood is still above the water surface as shown in diagram 2. The wood is then released and oscillates vertically. At the instant shown in diagram 3, the wood is moving downwards and the length of wood beneath the surface is d + x.

(i) On diagram 3, draw an arrow to show the direction of the acceleration of the wood. (1)

IB Questionbank Physics 22

(ii) The acceleration a of the wood (in m s2) is related to x (in m) by the following equation.

a = xl

14

Explain why this equation shows that the wood is executing simple harmonic motion.

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(iii) The period of oscillation of the wood is 1.4 s. Show that the length l of the wood is 0.70 m.

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IB Questionbank Physics 23

(b) The wood in (a), as shown in diagram 2, is released at time t = 0. On the axes below, sketch a graph to show how the velocity v of the wood varies with time over one period of oscillation.

(1)

(c) The distance A that the wood is initially pushed down is 0.12 m.

(i) Calculate the magnitude of the maximum acceleration of the wood.

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(ii) On your sketch graph in (b) label with the letter P one point where the magnitude of the acceleration is a maximum.

(1)

IB Questionbank Physics 24

(d) The oscillations of the wood generate waves in the water of wavelength 0.45 m. The graph shows how the displacement D, of the water surface at a particular distance from the wood varies with time t.

Using the graph, calculate the

(i) speed of the waves.

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(ii) ratio of the displacement at t = 1.75 s to the displacement at t = 0.35 s.

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IB Questionbank Physics 25

(iii) ratio of the energy of the wave at t = 1.75 s to the energy at t = 0.35 s

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(Total 15 marks)