This page contains the AQA A2 Physics Simple Harmonic Motion Questions and kerboodle answers for revision and understanding .This page also contains the link to the notes and video for the revision of this topic.
18.1 Oscillations AQA A2 Physics P18 Harmonic Motion Kerboodle Answers: Page No. 287
1
They jump off the platform and accelerate downwards due to gravity so their velocity steadily increases
-The rope starts to tighten and so applies a force of resistance to that of gravity so the jumper decelerates and his velocity decreases steadily
-When the force from the rope trying to pull them back up is equal to the force from gravity, the jumpers velocity goes to zero for an instance
-The rope now pulls them back up until it becomes slack, so their velocity is increasing
-Once the rope is slack it applies no more force the jumper and gravity dominates again so the velocity of the jumper decreases (even though they are still going upwards)
-The jumpers velocity will reach zero again as the they reach the platform again and they start to fall due to gravity (they will only reach the platform again if there is no energy loss during the jump, which in real life there is hence you never see bungee jumpers reach the platform again)
2 a
The oscillation of a body or system with its own natural frequency and under no external influence other than the impulse that initiated the motion
— called also free vibration
—opposed to forced oscillation
b
3 a its time period,
b its frequency of oscillation.
4 a X passes through equilibrium 0.2 s after Y passes through equilibrium in the same direction,
b X reaches maximum displacement at the same time as Y reaches maximum displacement in the opposite direction.
18.2 The principles of simple harmonic motion AQA A2 Physics P18 Harmonic Motion Kerboodle Answers : Page No. 289
1 a ¼ cycle later,
+25 mm, changing direction from up to down
b ½ cycle later,
0, moving down
c ¾ cycle later,
-25 mm, changing direction from down to up
d 1 cycle later?
0, moving up
2 a the frequency,
0.5Hz
b
i +25 mm,
-0.25ms-2
ii 0
0
iii —25 mm.
0.25ms-2
3 a its frequency,
0.5Hz
b its initial acceleration.
-0.32ms-2
4 a t = 1.0s,
-32mm 0.32ms-2
b t= 1.5s.
0, 0
18.3 More about sine waves AQA A2 Physics P18 Harmonic Motion Kerboodle Answers : Page No. 291
1 a its frequency,
0.33Hz
b its maximum acceleration.
0.25ms-2
2
a Determine:
i the amplitude,
12mm
ii the time period.
0.63 s
b 6.5mm
3 a its frequency,
2.1 Hz
b its amplitude.
0.057m
4 a its frequency,
3.7Hz
b i 0.10s,
-8.2 mm t0wards maximum negative displacement
ii s after its displacement was 412 mm.
-0.7 mm towards maximum positive displacement.
18.4 Applications of simple harmonic motion AQA A2 Physics P18 Harmonic Motion Kerboodle Answers : Page No. 295
g = 9.8 ms-2
1 a i its time period,
0.33 s
ii its frequency,
3.1 Hz
b its acceleration when its displacement was
0
ii 10 mm,
-3.7 ms-2
iii 20 mm.
-7.5 ms-2
2 a i the frequency,
3.0Hz
ii the time period of the oscillations.
0.33 s
b
f2
3 a Calculate:
i the extension of the spring at equilibrium,
70mm
ii the spring constant.
21 Nm-1
b of 1.9 Hz and calculate its period of oscillation.
0.53s
4 a Calculate:
i the force on the object at a displacement of 50 mm,
1.25N
ii the acceleration of the object at the instant it was released.
2.5ms-2
b i Show that the acceleration oat displacement x is given bg —SOX.
ii 1. 1 Hz, +47 mm
5 a Of length
i 1.0m,
2.0s
ii 0.25m.
1.0s
b 5.0s
6
18.5 Energy and simple harmonic motion AQA A2 Physics P18 Harmonic Motion Kerboodle Answers : Page No. 298
1 a i
1.50 s
ii 0.56 m
iii 0.029J
b Sketch graphs on the same axes to show how the potential energy and the kinetic energy of the pendulum vary with its displacement from equilibrium.
2
a i the spring constant k for the system,
60 N m-1
ii the time period Of the oscillations,
0.54s
b i 75mJ
ii 75mJ
iii 0.50m s-1
3 a i light
ii heavy
b Discuss how effective a car suspension damper would be, if the oil in the damper was replaced by oil that was much more viscous.
18.6 Forced vibrations and resonance AQA A2 Physics P18 Harmonic Motion Kerboodle Answers : Page No. 301
1 a i Resonance is a phenomenon that occurs when a given system is driven by another vibrating system or external force to oscillate with greater amplitude at a specific preferential frequency.
ii
Resonance involves a transfer of energy from the driving force to the oscillating object. This transfer will be a maximum when the force moves is in the same direction as the object is moving. This happens when both are moving together at the same frequency.
b
i increasing the mass,
Inverse relationship between resonant frequency and mass. It therefore decreases.
ii replacing the springs with stiffer springs.
For stiffer springs, the stiffness constant should increase. Therefore, resonant frequency increases.
2 A a the spring constant of the system,
b the frequency at which the system would resonate if the mass were doubled.
3 The panel of a washing machine vibrates loudly when the drum rotates at a particular frequency. Explain why this happens only when the drum rotates at this frequency.
4
The vehicle was still oscillating and that when the vehicle hits the second bump the applied frequency = the frequency that the vehicle is oscillating at
The speed bumps induce forced oscillations in the suspension of the car, the frequency of the speed bumps is equal to that of the natural frequency of the cars suspension thereby inducing resonance (producing large amplitude oscillations).
b 2.8 ms-1
Banner 1 Practice questions: Page No. 302-305
1 (a)
(i) With the object on the spring: the mean value of x = 72 mm, e = 70 mm
(ii) 1.4%
(b) (i) 0.551 s
(ii) 0.6%
(c) (i)
(ii) Hence show that T —27t — (3 marks)
(d)
Plot a suitable graph using the above measurements to confirm the equation and to determine g. (9 marks)
(e)
The graph should give a best-fit line that passes through the origin (or almost does). Without carrying out detailed error calculations, the percentage errors in the measurement of e and in T suggests an overall percentage error in g o fat least 2%, which would give an error in g of ± 0.2 m s−2.
The accepted value of g is within this range. An improved method of measuring the extension would give a more accurate value of g. Or the extension contributes the largest percentage error and improving this measurement is important.
For example, a convex lens could be used as a magnifying glass to observe the position of the marker pin on the mm scale.
2 (a) (i) Distance d is twice the amplitude.
(ii)
(b) (i)
(ii)
3
(a)
(b)
(c) Calculate the magnitude of the tension in the string when the mass passes through the lowest point of the first swing. (2 marks) AOA, 2003
4 (a)
(i)
(ii) Slate the direction in which the force acts. (3 marks)
Towards the centre of the turntable.
(b) (i)
(ii)
(c) Figure 5 is a graph of displacement against time for the pendulum.
Sketch, for the same interval, graphs of:
(i) acceleration against time for the bob, and
(ii) kinetic energy against time for the bob. (4 marks) AQA. 2005
5 (a)
(i)
The minus sign indicates that the acceleration is in the opposite direction to the displacement.
(ii) Copy Figure 6 and sketch the corresponding graph to show how the phase of velocity v relates to that of the acceleration a. (2 marks)
(b) (i)
(ii) When the mass on the spring is quite heavily damped its amplitude halves by the end of each complete cycle. Sketch a graph to show how the kinetic energy. E, (rnJ), of the mass on the spring varies with time, r over a single period.
Start at lime, t = 0, with your maximum kinetic energy.
You should include suitable values on each of your scales. (8 marks) AQA, 2004
6 (a) Forced vibrations/oscillations
(b)
- A structure has a natural frequency (or frequencies) of vibration.
- Resonance.
- This occurs when the frequency of a driving force is equal to a natural frequency of the structure.
- Large amplitude vibrations are then produced (or there is a large transfer of energy to the structure).
- This could damage the structure (or cause a bridge to fail).
(c)
- Install dampers (shock absorbers).
- Stiffen (or reinforce) the structure.
- Any other acceptable step e.g. redesign to change natural frequency, increase the mass of the bridge, restrict numbers of pedestrians.
7
(a) (i) Calculate the frequency of the oscillation.
(ii
Amplitude = 0.076 m (± 0.002 m)
(iii)
Damping does not alter the frequency but it does reduce the amplitude
(b) Draw on a copy of Figure 7 the displacement—time graph for a pendulum that has the same period and amplitude but oscillates 900 radian) out of phase with the one shown. (2 marks)
(c) (i) Maximum acceleration of bob
(ii)
8 (a (i)
(ii)
(b) With both masses still in place, the spring is now suspended from a horizontal support rod that can be made to oscillate vertically, as shown in Figure 8, with amplitude 30mm at several different frequencies.
Describe fully, with reference to amplitude, frequency and phase, the motion of the masses suspended from the spring in each of the following cases.
(i) The support rod oscillates at a frequency of 0.2
(ii) The support rod oscillates al a frequency of 1.5 Hz.
(iii) The support rod oscillates al a frequency 01 1 OHZ. (6 marks) AQA, 2006
- Forced vibrations at a frequency of 0.2 Hz are produced.
- The amplitude is similar to the driver’s (≈30mm) (or less than at resonance).
- The displacements of the masses are almost in phase with the displacements of the support rod. (at 1.5 Hz)
- Resonance is produced (or vibrations at a frequency of 1.5 Hz).
- The amplitude is very large (> 30 mm).
- The displacements of the masses have a phase lag of 90° on the displacements of the support rod.
- The motion may appear violent. (at 10 Hz)
- Forced vibrations at a frequency of 10 Hz are produced.
- The amplitude is small (<< 30 mm).
- The displacements of the masses have a phase lag of almost 180° on the displacements of the support rod.
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