17. Oscillations
A section of Physics, 9702
Listing 10 of 100 questions
A trolley on a track is attached by springs to fixed blocks X and Y, as shown in . The track contains many small holes through which air is blown vertically upwards. This results in the trolley resting on a cushion of air rather than being in direct contact with the track. springs L trolley holes track fixed block X Y fixed block The trolley is pulled to one side of its equilibrium position and then released so that it oscillates initially with simple harmonic motion. After a short time, the air blower is switched off. The variation with time t of the distance L of the trolley from block X is shown in . L / cm t / s Use to determine: the initial amplitude of the oscillations amplitude = cm the angular frequency ω of the oscillations ω = rad s–1 the maximum speed v0, in cm s–1, of the oscillating trolley. v0 = cm s–1 Apart from the quantities in , describe what may be deduced from about the motion of the trolley between time t = 0 and time t = 24 s. No calculations are required. On , sketch the variation with L of the velocity v of the trolley for its first complete oscillation. –10 –5 v / cm s–1 L / cm
9702_w21_qp_41
THEORY
2021
Paper 4, Variant 1
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A trolley on a smooth surface is attached by springs to fixed blocks as shown in . springs trolley smooth surface fixed block fixed block The trolley oscillates horizontally about its equilibrium position with an amplitude of 12 cm. shows the variation of the acceleration a of the trolley with displacement x from its equilibrium position. Friction between the trolley and the surface can be assumed to be negligible. 0.8 0.4 – 0.4 –0.8 – 4 –8 –12 x / cm a / m s–2 Describe the features of the line in that demonstrate that the motion of the trolley is simple harmonic. Use to determine the period T of the oscillations of the trolley. T = s On the line of the graph of , label with the letter P one point where the kinetic energy of the trolley is zero. On the line of the graph of , label with the letter Q an approximate position of one point where the kinetic energy of the trolley is equal to the potential energy stored in the springs.
9702_w21_qp_42
THEORY
2021
Paper 4, Variant 2
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A trolley on a track is attached by springs to fixed blocks X and Y, as shown in . The track contains many small holes through which air is blown vertically upwards. This results in the trolley resting on a cushion of air rather than being in direct contact with the track. springs L trolley holes track fixed block X Y fixed block The trolley is pulled to one side of its equilibrium position and then released so that it oscillates initially with simple harmonic motion. After a short time, the air blower is switched off. The variation with time t of the distance L of the trolley from block X is shown in . L / cm t / s Use to determine: the initial amplitude of the oscillations amplitude = cm the angular frequency ω of the oscillations ω = rad s–1 the maximum speed v0, in cm s–1, of the oscillating trolley. v0 = cm s–1 Apart from the quantities in , describe what may be deduced from about the motion of the trolley between time t = 0 and time t = 24 s. No calculations are required. On , sketch the variation with L of the velocity v of the trolley for its first complete oscillation. –10 –5 v / cm s–1 L / cm
9702_w21_qp_43
THEORY
2021
Paper 4, Variant 3
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An object is suspended from a spring that is attached to a fixed point as shown in . oscillations object spring equilibrium position fixed point The object oscillates vertically with simple harmonic motion about its equilibrium position. State the defining equation for simple harmonic motion. Identify the meaning of each of the symbols used to represent physical quantities. The variation with displacement x from the equilibrium position of the velocity v of the object is shown in . – 0.04 0.04 0.08 0.12 – 0.08 – 0.12 – 0.2 – 0.2 – 0.1 0.1 0.2 v / m s–1 x / m The variation with x of the potential energy EP of the oscillations of the object is shown in . – 0.04 0.04 0.08 0.12 – 0.08 – 0.12 0.025 0.050 x / m EP / J Use and to: determine the amplitude x0 of the oscillations x0 = m show that the angular frequency of the oscillations is 1.7 rad s–1 determine the mass M of the object. M = kg The oscillations of the object are now lightly damped. State what is meant by damping. Assume that the damping does not change the angular frequency of the oscillations. On , sketch the variation with x of v when the amplitude of the oscillations is 0.060 m.
9702_w22_qp_41
THEORY
2022
Paper 4, Variant 1
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An object is suspended from a spring that is attached to a fixed point as shown in . oscillations object spring equilibrium position fixed point The object oscillates vertically with simple harmonic motion about its equilibrium position. State the defining equation for simple harmonic motion. Identify the meaning of each of the symbols used to represent physical quantities. The variation with displacement x from the equilibrium position of the velocity v of the object is shown in . – 0.04 0.04 0.08 0.12 – 0.08 – 0.12 – 0.2 – 0.2 – 0.1 0.1 0.2 v / m s–1 x / m The variation with x of the potential energy EP of the oscillations of the object is shown in . – 0.04 0.04 0.08 0.12 – 0.08 – 0.12 0.025 0.050 x / m EP / J Use and to: determine the amplitude x0 of the oscillations x0 = m show that the angular frequency of the oscillations is 1.7 rad s–1 determine the mass M of the object. M = kg The oscillations of the object are now lightly damped. State what is meant by damping. Assume that the damping does not change the angular frequency of the oscillations. On , sketch the variation with x of v when the amplitude of the oscillations is 0.060 m.
9702_w22_qp_43
THEORY
2022
Paper 4, Variant 3
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A heavy metal sphere of mass 0.81 kg is suspended from a string. The sphere is undergoing small oscillations from side to side, as shown in . string heavy sphere, mass 0.81 kg oscillations The oscillations of the sphere may be considered to be simple harmonic with amplitude 0.036 m and period 3.0 s. State what is meant by simple harmonic motion. Calculate: the angular frequency of the oscillations angular frequency = rad s–1 the total energy of the oscillations. total energy = J The suspended sphere is now lowered into water. The sphere is given a sideways displacement of +0.036 m from its equilibrium position and is then released at time t = 0. The water causes the motion of the sphere to be critically damped. On , sketch the variation of the displacement x of the sphere from its equilibrium position with t from t = 0 to t = 6.0 s. 0.02 0.04 – 0.02 – 0.04 x / m t / s
9702_w23_qp_41
THEORY
2023
Paper 4, Variant 1
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A heavy metal sphere of mass 0.81 kg is suspended from a string. The sphere is undergoing small oscillations from side to side, as shown in . string heavy sphere, mass 0.81 kg oscillations The oscillations of the sphere may be considered to be simple harmonic with amplitude 0.036 m and period 3.0 s. State what is meant by simple harmonic motion. Calculate: the angular frequency of the oscillations angular frequency = rad s–1 the total energy of the oscillations. total energy = J The suspended sphere is now lowered into water. The sphere is given a sideways displacement of +0.036 m from its equilibrium position and is then released at time t = 0. The water causes the motion of the sphere to be critically damped. On , sketch the variation of the displacement x of the sphere from its equilibrium position with t from t = 0 to t = 6.0 s. 0.02 0.04 – 0.02 – 0.04 x / m t / s
9702_w23_qp_43
THEORY
2023
Paper 4, Variant 3
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State what is meant by simple harmonic motion. A block is suspended from a spring, as shown in . spring block floor h The block is pulled down and released at time t = 0. It then oscillates vertically with simple harmonic motion. shows the variation of the velocity v of the block with height h of the base of the block above the floor. –10 –5 v / cm s–1 h / cm Determine the amplitude, in cm, of the oscillations. amplitude = cm Show that the angular frequency of the oscillations is 3.2 rad s–1. Calculate the period T of the oscillations. T = s On , sketch the variation of h with time t from t = 0 to t = 6.0 s. t / s 2.5 5.0 h / cm 7.5 10.0
9702_w24_qp_41
THEORY
2024
Paper 4, Variant 1
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shows a pendulum consisting of a metal sphere suspended by a thin string. thin string metal sphere oscillations (not to scale) The sphere undergoes small oscillations about its equilibrium position. The oscillations may be considered to be simple harmonic. shows the variation with time t of the displacement x of the sphere from its equilibrium position. –0.02 x / m –0.01 0.01 0.02 0.2 0.4 0.6 t / s 0.8 1.0 1.2 On , draw an arrow, from the centre of the sphere, to represent the direction of the resultant force acting on the sphere when it is in the position shown. The mass of the sphere is 0.15 kg. State the amplitude of the oscillations. amplitude = m Determine the angular frequency of the oscillations. angular frequency = rad s–1 Calculate the total energy of the oscillations. total energy = J On , sketch the variation with x of the kinetic energy EK of the sphere. x / m –0.02 –0.01 0.01 0.02 EK / 10–3 J
9702_w24_qp_42
THEORY
2024
Paper 4, Variant 2
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Questions Discovered
100