6 questions · 35 marks · ≈ 35 min
A mass is hung from a spring and set into vertical oscillation by displacing the mass 5 cm from its equilibrium position.
The graph shows how the acceleration a of the mass depends upon the displacement *x *of the mass from its equilibrium position.
Sketch a graph on the axes below to show how x depends upon time t.
A music system has a number of loudspeakers. One loudspeaker produces the low frequency sounds. This loudspeaker consists of a coil connected to a cone. The coil is in a region of magnetic field produced by a permanent magnet, as shown.
A signal of constant frequency is applied to the loudspeaker. The coil moves with simple harmonic motion and the loudspeaker emits a sound of frequency 75 Hz.
When the loudspeaker is producing this sound, the coil moves through a maximum distance of 3.5 mm.
i) Calculate the maximum velocity of the coil.
Maximum velocity of the coil = .............................(3)
ii) State the position of the coil when the velocity is a maximum.
(1 mark)
At a particular frequency, the loudspeaker cone starts to oscillate with a very large amplitude.
Explain why this effect is observed.
A website advertises a baby crib that can be hung from a spring. The crib can be set into vertical oscillation.
The instructions for the crib state that the crib can support a maximum mass of 15.0 kg.
i) When the crib supports a mass of 15.0 kg the spring extends by 42.5 cm.
Show that the stiffness of the spring is about 350 N m−1.
(2 marks)
ii) A baby is placed in the crib and the spring extends to bring the system to equilibrium. The crib is displaced through a small vertical displacement and released.
State why the crib will oscillate with simple harmonic motion.
(2 marks)
iii) The baby has a mass of 7.25 kg.
Calculate the period of oscillation of the crib.
mass of crib = 2.55 kg
stiffness of spring = 350 Nm−1
Period of oscillation of crib = .....................................(2)
The maximum mass that the spring can support before being damaged is 25.0 kg.
Explain why the instructions state that the maximum mass is only 15.0 kg.
A student set up a simple pendulum. The student used a velocity sensor connected to a data logger to record the velocity of the pendulum bob.
The graph shows how the velocity of the bob varied with time.
i) Add a line to the graph to show how the displacement of the bob varied with time during the same time interval.
(2 marks)
ii) Determine the length of the simple pendulum.
Length of simple pendulum = ........................................(3)
In some experiments, it is an advantage to use a data logger rather than other measuring instruments.
Describe when the use of a data logger is an advantage.
A student suspended a spring from a rigid support. She stretched the spring by hanging a mass from the free end of the spring as shown.
She set the mass into vertical oscillations by displacing it a small distance from its equilibrium position. The spring obeys Hooke’s law.
Explain why the mass moves with simple harmonic motion.
A student suspended a spring from a rigid support. She stretched the spring by hanging a mass from the free end of the spring as shown.
She set the mass into vertical oscillations by displacing it a small distance from its equilibrium position. The spring obeys Hooke’s law.
When the mass on the end of the spring was 0.200 kg, the extension of the spring was 7.50 cm when the mass was in equilibrium.
i) Show that the stiffness k of the spring is about 26 Nm−1.
(2 marks)
ii) The student used a stopwatch to determine the frequency of oscillation f of the mass m.
She repeated this procedure for four more values of m and obtained the following graph.
The student used the graph to determine a value for k.
Deduce whether the graph gives a value of k consistent with the value in (i).
(6 marks)