Topic questions Forces Simple harmonic motion
18 questions · 130 marks · about 2.5 hours
A trolley is attached to two springs and set into horizontal oscillation, as shown.
The kinetic energy of the trolley is Ek, and the potential energy of the trolley is Ep. Which row of the table is correct?
Also involves Gravity and weight
The photograph shows the Petronas Twin Towers in Kuala Lumpur, which are the world’s tallest twin buildings.
Each tower is supported by 16 cylindrical concrete columns.
Calculate the stress at the base of each cylindrical concrete column.
mass of each tower = 3.0
108kg diameter of each column = 2.4 m
Tall buildings sway in the wind. The design of the Petronas Towers permits safe movement of the towers.
The towers were designed to permit a maximum horizontal displacement of 0.90 m at the top of the towers. The natural frequency of each tower is 0.17 Hz.
Calculate the maximum velocity at the top of one of the towers when the tower is oscillating at its natural frequency.
The twin towers were linked together to improve the response of the building to strong winds.
The graph below shows how the maximum displacement x varies with the frequency f for a single tower and for two linked towers.
Explain the behaviour of a single tower compared with the behaviour of the linked towers.
A mass is suspended from a spring and displaced vertically. The mass performs simple harmonic motion.
The graph shows how the acceleration of the mass varies with time over one oscillation.
Which of the following graphs shows how the velocity v of the mass varies with time t over the same time interval?
On the International Space Station (ISS), astronauts measure their mass once a month using a Body Mass Measurement Device (BMMD).
The BMMD is constructed from a large spring attached to the floor of the ISS, with a platform and handles attached to the spring. The spring is compressed and the astronaut puts his body onto the platform and holds onto the handles, as shown.
(Source: https://www.nasa.gov/content/nasa-astronaut-rick-mastracchio-3)
The spring is released and the astronaut and platform oscillate with simple harmonic motion.
An astronaut used the BMMD. The frequency of oscillation was 0.34 Hz.
Determine the mass of the astronaut.
spring constant = 350 N m–1 mass of platform = 5.7 kg
The distance between the upper and lower points of the first oscillation is 0.29 m.
Calculate the magnitude of the maximum acceleration of the astronaut.
Calculate the speed of the astronaut 3.5 s after the start of the oscillations.
A ‘jumperoo’ is a harness, suspended by a vertical spring, into which a baby can be placed, as shown.
The jumperoo is adjusted so that the baby’s feet are a few centimetres above the floor. If the baby is then displaced downwards and released, he oscillates vertically.
The graph shows how the acceleration a of the baby depends upon the displacement x of the baby from its equilibrium position.
For safety reasons, it is suggested that the maximum velocity of the baby should not
Assess whether it is safe for the baby to oscillate in the jumperoo with an amplitude of 22 cm.
The amplitude of the oscillations quickly decreases, so the baby has to push down on the floor to maintain the oscillations.
When the baby pushes at a particular frequency, the amplitude of oscillation increases to a maximum.
A baby of greater mass is placed in the jumperoo.
This baby pushes on the floor at a frequency that produces a maximum amplitude of oscillation.
Explain how this frequency compares with the frequency of pushing of the original baby.
A calculation is not necessary.
An object oscillates with simple harmonic motion. The object has kinetic energy Ek and displacement x.
Which of the following graphs shows the variation of Ek with x for the object?
The suspension system in a car includes a spring attached to each wheel as shown.
The car, of mass 1100 kg, is stationary. Each spring is compressed by 152 mm due to a quarter of the weight of the car. Each spring is well within both the limit of proportionality and the elastic limit.
State what is meant by within the elastic limit.
Show that the stiffness of each spring is about 18 000 N m–1.
A force is applied to the car which results in a further small compression of each spring. The force is then removed, and the body of the car oscillates with simple harmonic motion.
Determine the frequency of the oscillations.
State the conditions for simple harmonic motion.
The oscillations are heavily damped by a piston in the suspension system. The piston moves within a cylinder filled with oil, as shown. The oil has a high viscosity.
Explain why using oil of high viscosity will produce heavy damping.
A student investigated the horizontal oscillations of a trolley between two springs, using the apparatus shown.
The student displaced the trolley from its equilibrium position. She then released the trolley and started a stopwatch. She stopped the stopwatch when the trolley had completed one oscillation.
Describe how the method used by the student could be improved to determine a more accurate value of the time period.
The student displaced the trolley 6.0 cm from the equilibrium position. She recorded the velocity of the oscillating trolley using a sensor connected to a data logger.
The output from the data logger is shown below.
The time-base of the data logger output was set to 250 ms div–1.
Determine the maximum velocity of the trolley.
Explain the shape of the graph.
Determine the effective spring constant k of the oscillating trolley system.
mass of trolley = 0.87 kg
A garden ornament consists of a metal flamingo suspended from a spring as shown. The spring is hung from a support using the hook.
The mass of the flamingo is 65 g. When the flamingo is suspended vertically the spring extends by 8.5 cm.
The flamingo is pulled downwards by a small extra displacement and then released. The flamingo undergoes simple harmonic motion vertically.
The instructions state that the flamingo will oscillate with a frequency of 2.5 Hz.
Deduce whether this statement is correct.
After being set into vertical oscillation, the flamingo comes to rest after a short time.
Explain why the flamingo comes to rest.
In a slight breeze the flamingo swings from side to side and behaves as a simple pendulum.
Show that the period of oscillation of the flamingo pendulum is about 2.2 s.
pendulum length = 1.25 m
The amplitude of oscillation of the flamingo pendulum is 7.5 cm.
Calculate the maximum velocity of the flamingo pendulum.
In 2011, a tsunami was caused by a massive earthquake centred some distance off the coast of Japan. The tsunami caused a cooling system failure at the Fukushima Nuclear Power Plant. This resulted in a nuclear meltdown and radioactive materials were released into the surroundings.
A reservoir beside one of the reactor buildings contained a large volume of water. In 2013, this water was found to have an extremely high concentration of caesium-137. Caesium-137 is a radioactive isotope of caesium.
Complete the nuclear equation for the decay of caesium-137.
An activity of 2.35 × 1012 Bq per m3 of water in the reservoir was measured. It is suggested that a safe level for the activity of all water in the reservoir would be 100 Bq.
Calculate the time in years for the caesium-137 to decay to a safe level.
volume of water in reservoir = 5000 m3 half-life of caesium-137 = 30 years
The most common radionuclide amongst the fission products in the fuel was iodine-131, which decays with a half-life of 8.0 days to form a stable isotope of the gas xenon.
Deduce whether enough xenon would have collected in 32 days to exert a pressure of 1.0 
105 Pa in a volume of 450 m3. Assume that no gas escapes.
temperature = 20 °C initial number of iodine nuclei = 1.25 × 1028
Buildings in nearby Tohoku University suffered structural damage during the 2011 earthquake.
The graph shows how the acceleration of one of the buildings, measured on the 9th floor, varied with time during the earthquake.
(Source: https://www.sciencedirect.com/science/article/pii/S0038080612001035)
At the time it was reported that during the earthquake the 9th floor of the building displaced by more than 30 cm from its normal position.
Assess the accuracy of this report.
Also involves Newton's laws of motion
A mass is suspended from a spring and allowed to come to equilibrium. The mass is displaced vertically and moves with simple harmonic motion. The graph shows how the resultant force on the mass varies with time.
Which of the following graphs shows how the velocity v of the mass varies with time t over the same time interval?
A simple pendulum consisting of a thread and a bob is set up next to a horizontal rod.
The bob is displaced to the left and released. When the bob reaches the equilibrium position the thread strikes the horizontal rod. For half of the cycle, only the lower part of the pendulum moves.
The diagram shows the swing of the pendulum.
The diagram below shows the dimensions of the pendulum.
Determine the frequency of the oscillations of the pendulum.
A student measured the deflection of a mass attached to the end of a thin strip of metal. The strip was clamped to a bench at one end as shown.
The student varied the force on the end of the strip by changing the mass attached.
The deflection was measured each time when the mass was in its equilibrium position.
The student obtained the following graph of deflection against force.
State why the mass will oscillate with simple harmonic motion when it is displaced slightly from its equilibrium position and released.
The student then investigated the oscillations of the mass on the metal strip. The student fixed different numbers of 10 g masses to the end of the metal strip.
The student noticed that the smaller the mass the higher the frequency of the oscillations. He estimated that the maximum number of oscillations he could count was two per second. He decided that the smallest mass he should use was 50 g.
Determine whether 50 g is the smallest mass he should use.
You may assume that the system acts in the same way as a mass on a spring.
A student measured the deflection of a mass attached to the end of a thin strip of metal. The strip was clamped to a bench at one end as shown.
The student varied the force on the end of the strip by changing the mass attached.
The deflection was measured each time when the mass was in its equilibrium position.
The student obtained the following graph of deflection against force.
State why the mass will oscillate with simple harmonic motion when it is displaced slightly from its equilibrium position and released.
The student then investigated the oscillations of the mass on the metal strip. The student fixed different numbers of 10 g masses to the end of the metal strip.
The student noticed that the smaller the mass the higher the frequency of the oscillations. He estimated that the maximum number of oscillations he could count was two per second. He decided that the smallest mass he should use was 50 g.
Determine whether 50 g is the smallest mass he should use.
You may assume that the system acts in the same way as a mass on a spring.
A trolley is attached to the ends of two springs as shown. When displaced from its equilibrium position, the trolley moves with simple harmonic motion.
A student has a stopwatch and metre rule available.
Explain the procedure that the student should follow to make an accurate determination of the time period T of the trolley.
Describe how the student should use her value of T to determine the maximum speed of the trolley.
Another student suggests that a more accurate value for T could be obtained by using a position sensor and data logger.
Comment on this suggestion.
The student displaces the trolley a greater distance from the equilibrium position, so the amplitude of oscillation is doubled. The trolley still moves with simple harmonic motion.
Explain how the maximum kinetic energy of the trolley will change.
The International Space Station (ISS) is in a low Earth orbit. Astronauts in ISS have an apparent weight of zero. In order to determine their mass, the astronauts must secure themselves to a platform which is set into oscillation and moves with simple harmonic
Explain why the astronauts in the ISS have an apparent weight of zero.
State what is meant by simple harmonic motion.
Describe how, using a stopwatch and a ruler, the following quantities could be determined for the oscillating platform:
the frequency of oscillation
the maximum speed of the platform.
The platform continues to move with simple harmonic motion at the same frequency, but its amplitude is doubled.
Explain how the maximum kinetic energy of the platform will change.
A playground swing completes 24 oscillations in 1 minute.
Which of the following is the frequency of the oscillations?
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