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17. Oscillations
A section of Physics, 9702
Listing 10 of 100 questions
State, by reference to displacement, what is meant by simple harmonic motion. A mass is undergoing oscillations in a vertical plane. The variation with displacement x of the acceleration a of the mass is shown in . a x State two reasons why the motion of the mass is not simple harmonic. 1. 2. A block of wood is floating in a liquid, as shown in . oscillation of block liquid block The block is displaced vertically and then released. The variation with time t of the displacement y of the block from its equilibrium position is shown in . 0.4 0.8 1.2 1.6 2.0 2.4 2.0 1.5 1.0 0.5 –0.5 –1.0 –1.5 –2.0 t / s y / cm Use data from to determine the angular frequency ω of the oscillations, ω = rad s−1 the maximum vertical acceleration of the block. maximum acceleration = m s−2 The block has mass 120 g. The oscillations of the block are damped. Calculate the loss in energy of the oscillations of the block during the first three complete periods of its oscillations. energy loss = J
9702_s16_qp_41
THEORY
2016
Paper 4, Variant 1
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A metal block hangs vertically from one end of a spring. The other end of the spring is tied to a thread that passes over a pulley and is attached to a vibrator, as shown in . spring block pulley vibrator The vibrator is switched off. The metal block of mass 120 g is displaced vertically and then released. The variation with time t of the displacement y of the block from its equilibrium position is shown in . –3 –2 –1 y / cm 0.2 0.4 0.6 0.8 1.0 W / s For the vibrations of the block, calculate the angular frequency ω, ω = rad s−1 the energy of the vibrations. energy = J The vibrator is now switched on. The frequency of vibration is varied from 0.7f to 1.3f where f is the frequency of vibration of the block in . For the block, complete to show the variation with frequency of the amplitude of vibration. Label this line A. amplitude 0.7I I 1.3I frequency Some light feathers are now attached to the block in to increase air resistance. The frequency of vibration is once again varied from 0.7f to 1.3f. The new amplitude of vibration is measured for each frequency. On , draw a line to show the variation with frequency of the amplitude of vibration. Label this line B.
9702_s16_qp_42
THEORY
2016
Paper 4, Variant 2
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State, by reference to displacement, what is meant by simple harmonic motion. A mass is undergoing oscillations in a vertical plane. The variation with displacement x of the acceleration a of the mass is shown in . a x State two reasons why the motion of the mass is not simple harmonic. 1. 2. A block of wood is floating in a liquid, as shown in . oscillation of block liquid block The block is displaced vertically and then released. The variation with time t of the displacement y of the block from its equilibrium position is shown in . 0.4 0.8 1.2 1.6 2.0 2.4 2.0 1.5 1.0 0.5 –0.5 –1.0 –1.5 –2.0 t / s y / cm Use data from to determine the angular frequency ω of the oscillations, ω = rad s−1 the maximum vertical acceleration of the block. maximum acceleration = m s−2 The block has mass 120 g. The oscillations of the block are damped. Calculate the loss in energy of the oscillations of the block during the first three complete periods of its oscillations. energy loss = J
9702_s16_qp_43
THEORY
2016
Paper 4, Variant 3
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A bar magnet of mass 180 g is suspended from the free end of a spring, as illustrated in . spring magnet coil The magnet hangs so that one pole is near the centre of a coil of wire. The coil is connected in series with a resistor and a switch. The switch is open. The magnet is displaced vertically and then allowed to oscillate with one pole remaining inside the coil. The other pole remains outside the coil. At time t = 0, the magnet is oscillating freely as it passes through its equilibrium position. At time t = 3.0 s, the switch in the circuit is closed. The variation with time t of the vertical displacement y of the magnet is shown in . –2.0 –1.5 –1.0 –0.5 0.5 1.0 y / cm 1.5 2.0 t / s Determine, to two significant figures, the frequency of oscillation of the magnet. frequency = Hz State whether the closing of the switch gives rise to light, heavy or critical damping. Calculate the change in the energy ΔE of oscillation of the magnet between time t = 2.7 s and time t = 7.5 s. Explain your working. ΔE = J
9702_s17_qp_41
THEORY
2017
Paper 4, Variant 1
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A bar magnet of mass 180 g is suspended from the free end of a spring, as illustrated in . spring magnet coil The magnet hangs so that one pole is near the centre of a coil of wire. The coil is connected in series with a resistor and a switch. The switch is open. The magnet is displaced vertically and then allowed to oscillate with one pole remaining inside the coil. The other pole remains outside the coil. At time t = 0, the magnet is oscillating freely as it passes through its equilibrium position. At time t = 3.0 s, the switch in the circuit is closed. The variation with time t of the vertical displacement y of the magnet is shown in . –2.0 –1.5 –1.0 –0.5 0.5 1.0 y / cm 1.5 2.0 t / s Determine, to two significant figures, the frequency of oscillation of the magnet. frequency = Hz State whether the closing of the switch gives rise to light, heavy or critical damping. Calculate the change in the energy ΔE of oscillation of the magnet between time t = 2.7 s and time t = 7.5 s. Explain your working. ΔE = J
9702_s17_qp_43
THEORY
2017
Paper 4, Variant 3
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A metal plate is made to vibrate vertically by means of an oscillator, as shown in . direction of oscillations sand plate oscillator Some sand is sprinkled on to the plate. The variation with displacement y of the acceleration a of the sand on the plate is shown in . –10 y / mm a / m s–2 –5 –4 –3 –2 –1 –8 –6 –4 –2 Use to show how it can be deduced that the sand is undergoing simple harmonic motion. Calculate the frequency of oscillation of the sand. frequency = Hz The amplitude of oscillation of the plate is gradually increased beyond 8 mm. The frequency is constant. At one amplitude, the sand is seen to lose contact with the plate. For the plate when the sand first loses contact with the plate, state the position of the plate, calculate the amplitude of oscillation. amplitude = mm
9702_s18_qp_41
THEORY
2018
Paper 4, Variant 1
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State two conditions necessary for a mass to be undergoing simple harmonic motion. 1. 2. A trolley of mass 950 g is held on a horizontal surface by means of two springs attached to fixed points P and Q, as shown in . Q P trolley mass 950 g spring The springs, each having a spring constant k of 230 N m–1, are always extended. The trolley is displaced along the line of the springs and then released. The variation with time t of the displacement x of the trolley is shown in . x t1 t 1. State and explain whether the oscillations of the trolley are heavily damped, critically damped or lightly damped. 2. Suggest the cause of the damping. The acceleration a of the trolley of mass m may be assumed to be given by the expression a = – m k x d n . 1. Calculate the angular frequency ω of the oscillations of the trolley. ω = rad s–1 2. Determine the time t1 shown on . t1 = s
9702_s18_qp_42
THEORY
2018
Paper 4, Variant 2
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A metal plate is made to vibrate vertically by means of an oscillator, as shown in . direction of oscillations sand plate oscillator Some sand is sprinkled on to the plate. The variation with displacement y of the acceleration a of the sand on the plate is shown in . –10 y / mm a / m s–2 –5 –4 –3 –2 –1 –8 –6 –4 –2 Use to show how it can be deduced that the sand is undergoing simple harmonic motion. Calculate the frequency of oscillation of the sand. frequency = Hz The amplitude of oscillation of the plate is gradually increased beyond 8 mm. The frequency is constant. At one amplitude, the sand is seen to lose contact with the plate. For the plate when the sand first loses contact with the plate, state the position of the plate, calculate the amplitude of oscillation. amplitude = mm
9702_s18_qp_43
THEORY
2018
Paper 4, Variant 3
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A hollow tube, sealed at one end, has a cross-sectional area A of 24 cm2. The tube contains sand so that the total mass M of the tube and sand is 0.23 kg. The tube floats upright in a liquid of density t, as illustrated in . liquid, density t tube, area of cross-section A h sand The depth of the bottom of the tube below the liquid surface is h. The tube is displaced vertically and then released. The variation with time t of the depth h is shown in . 0.2 0.4 0.6 0.8 1.0 1.2 1.4 t / s h / cm Determine: the amplitude, in metres, of the oscillations amplitude = m the frequency of oscillation of the tube in the liquid frequency = Hz the acceleration of the tube when h is a maximum. acceleration = m s–2 The frequency f of oscillation of the tube is given by the expression f = 1 2π M A g c m t where g is the acceleration of free fall. Calculate the density t of the liquid in which the tube is floating. t = kg m–3 The oscillations illustrated in are undamped. In practice, the liquid does cause light damping. On , draw a line to show light damping of the oscillations for time t = 0 to time t = 1.4 s.
9702_s19_qp_41
THEORY
2019
Paper 4, Variant 1
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Questions Discovered
100