17. Oscillations
A section of Physics, 9702
Listing 10 of 100 questions
The variation with displacement x of the acceleration a of the centre of the cone of a loudspeaker is shown in . –0.3 –0.2 –0.1 0.1 0.2 0.3 –750 –500 –250 a / m s–2 x / mm State the two features of that show that the motion of the cone is simple harmonic. 1. 2. Use data from to determine the frequency, in hertz, of vibration of the cone. frequency = Hz The frequency of vibration of the cone is now reduced to one half of that calculated in . The amplitude of vibration remains unchanged. On the axes of , draw a line to represent the variation with displacement x of the acceleration a of the centre of the loudspeaker cone.
9702_w09_qp_42
THEORY
2009
Paper 4, Variant 2
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A student sets up the apparatus illustrated in in order to investigate the oscillations of a metal cube suspended on a spring. variable-frequency oscillator thread pulley spring metal cube The amplitude of the vibrations produced by the oscillator is constant. The variation with frequency of the amplitude of the oscillations of the metal cube is shown in . amplitude / mm frequency / Hz State the phenomenon illustrated in . For the maximum amplitude of vibration, state the magnitudes of the amplitude and the frequency. amplitude = mm frequency = Hz The oscillations of the metal cube of mass 150 g may be assumed to be simple harmonic. Use your answers in to determine, for the metal cube, its maximum acceleration, acceleration = m s–2 the maximum resultant force on the cube. force = N Some very light feathers are attached to the top surface of the cube so that the feathers extend outwards, beyond the vertical sides of the cube. The investigation is now repeated. On , draw a line to show the new variation with frequency of the amplitude of vibration for frequencies between 2 Hz and 10 Hz.
9702_w10_qp_41
THEORY
2010
Paper 4, Variant 1
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A student sets up the apparatus illustrated in in order to investigate the oscillations of a metal cube suspended on a spring. variable-frequency oscillator thread pulley spring metal cube The amplitude of the vibrations produced by the oscillator is constant. The variation with frequency of the amplitude of the oscillations of the metal cube is shown in . amplitude / mm frequency / Hz State the phenomenon illustrated in . For the maximum amplitude of vibration, state the magnitudes of the amplitude and the frequency. amplitude = mm frequency = Hz The oscillations of the metal cube of mass 150 g may be assumed to be simple harmonic. Use your answers in to determine, for the metal cube, its maximum acceleration, acceleration = m s–2 the maximum resultant force on the cube. force = N Some very light feathers are attached to the top surface of the cube so that the feathers extend outwards, beyond the vertical sides of the cube. The investigation is now repeated. On , draw a line to show the new variation with frequency of the amplitude of vibration for frequencies between 2 Hz and 10 Hz.
9702_w10_qp_42
THEORY
2010
Paper 4, Variant 2
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A cylinder and piston, used in a car engine, are illustrated in . C A D cylinder piston B The vertical motion of the piston in the cylinder is assumed to be simple harmonic. The top surface of the piston is at AB when it is at its lowest position; it is at CD when at its highest position, as marked in . The displacement d of the piston may be represented by the equation d = – 4.0 cos(220t ) where d is measured in centimetres. State the distance between the lowest position AB and the highest position CD of the top surface of the piston. distance = cm Determine the number of oscillations made per second by the piston. number = On , draw a line to represent the top surface of the piston in the position where the speed of the piston is maximum. Calculate the maximum speed of the piston. speed = cm s–1 The engine of a car has several cylinders. Three of these cylinders are shown in . C A D B X Y Z X is the same cylinder and piston as in . Y and Z are two further cylinders, with the lowest and the highest positions of the top surface of each piston indicated. The pistons in the cylinders each have the same frequency of oscillation, but they are not in phase. At a particular instant in time, the position of the top of the piston in cylinder X is as shown. In cylinder Y, the oscillations of the piston lead those of the piston in cylinder X by a phase angle of 120° (2 3p rad). Complete the diagram of cylinder Y, for this instant, by drawing 1. a line to show the top surface of the piston, 2. an arrow to show the direction of movement of the piston. In cylinder Z, the oscillations of the piston lead those of the piston in cylinder X by a phase angle of 240° (4 3p rad). Complete the diagram of cylinder Z, for this instant, by drawing 1. a line to show the top surface of the piston, 2. an arrow to show the direction of movement of the piston. For the piston in cylinder Y, calculate its speed for this instant. speed = cm s–1
9702_w10_qp_43
THEORY
2010
Paper 4, Variant 3
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Define simple harmonic motion. A horizontal plate is vibrating vertically, as shown in . vertical oscillations frequency 4.5 Hz cube, mass 5.8 g plate The plate undergoes simple harmonic motion with a frequency of 4.5 Hz and amplitude 3.0 mm. A metal cube of mass 5.8 g rests on the plate. Calculate, for the cube, the energy of oscillation. energy = J The amplitude of oscillation of the plate in is gradually increased. The frequency remains constant. At one particular amplitude, the cube just loses contact momentarily with the plate. State the position of the plate in its oscillation at the point when the cube loses contact. Calculate this amplitude of oscillation. amplitude = m
9702_w11_qp_43
THEORY
2011
Paper 4, Variant 3
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A ball is held between two fixed points A and B by means of two stretched springs, as shown in . ball A B The ball is free to oscillate horizontally along the line AB. During the oscillations, the springs remain stretched and do not exceed their limits of proportionality. The variation of the acceleration a of the ball with its displacement x from its equilibrium position is shown in . –3 –5 –10 –15 –2 –1 x / cm a / m s–2 State and explain the features of that indicate that the motion of the ball is simple harmonic. Use to determine, for the oscillations of the ball, the amplitude, amplitude = cm the frequency. frequency = Hz The arrangement in is now rotated through 90° so that the line AB is vertical. The ball now oscillates in a vertical plane. Suggest one reason why the oscillations may no longer be simple harmonic.
9702_w12_qp_41
THEORY
2012
Paper 4, Variant 1
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A ball is held between two fixed points A and B by means of two stretched springs, as shown in . ball A B The ball is free to oscillate horizontally along the line AB. During the oscillations, the springs remain stretched and do not exceed their limits of proportionality. The variation of the acceleration a of the ball with its displacement x from its equilibrium position is shown in . –3 –5 –10 –15 –2 –1 x / cm a / m s–2 State and explain the features of that indicate that the motion of the ball is simple harmonic. Use to determine, for the oscillations of the ball, the amplitude, amplitude = cm the frequency. frequency = Hz The arrangement in is now rotated through 90° so that the line AB is vertical. The ball now oscillates in a vertical plane. Suggest one reason why the oscillations may no longer be simple harmonic.
9702_w12_qp_42
THEORY
2012
Paper 4, Variant 2
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A metal ball is suspended from a fixed point by means of a string, as illustrated in . x ball string The ball is given a small displacement and then released. The variation with time t of the displacement x of the ball is shown in . –1.0 1.0 x / cm 2.0 –2.0 0.4 0.8 1.2 1.6 2.0 t / s State two times at which the speed of the ball is a maximum. time = s and time = s Show that the maximum speed of the ball is approximately 0.08 m s–1. The variation with displacement x of the potential energy EP of the oscillations of the ball is shown in . –1.0 –1.5 –0.5 0.5 1.0 1.5 x / cm energy / mJ EP On the axes of , sketch a graph to show the variation with displacement x of the kinetic energy of the ball. The amplitude of the oscillations reduces over a long period of time. After many oscillations, the amplitude of the oscillations is 0.60 cm. Use to determine the total energy of the oscillations of the ball for oscillations of amplitude 0.60 cm. Explain your working. energy = J
9702_w13_qp_41
THEORY
2013
Paper 4, Variant 1
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Questions Discovered
100