Extract:
When marking this question:
- Accept "forcing frequency" or "frequency of the applied force" for "driving frequency"
- Accept "the frequency at which the system oscillates freely" as a description of natural frequency
- Do not accept "large amplitude" without reference to a maximum
A washing machine rests on spring mounts. During the spin cycle, the wet clothes in the rotating drum are not evenly distributed, so the drum exerts a periodic force on the machine. The frequency of this force is equal to the rotation frequency of the drum.
The machine and its contents can be modelled as a mass–spring system oscillating vertically. The mounts obey Hooke's law.
Explain what is meant by resonance.
Extract:
A washing machine rests on spring mounts. During the spin cycle, the wet clothes in the rotating drum are not evenly distributed, so the drum exerts a periodic force on the machine. The frequency of this force is equal to the rotation frequency of the drum.
The machine and its contents can be modelled as a mass–spring system oscillating vertically. The mounts obey Hooke's law.
The mass of the empty washing machine is 72 kg. When wet clothes of mass 8.0 kg are placed in the drum, the machine sinks a further 2.0 mm on its mounts.
Calculate the rotation rate of the drum, in revolutions per minute, at which resonance occurs.
Extract:
Calculate the rotation rate of the drum, in revolutions per minute, at which resonance occurs.
Mark scheme result from (b): rotation rate = 210 rev min-1 (the natural frequency of the machine as a mass-spring system, f₀ = 3.5 Hz).
When marking this question:
- For the first mark, accept: the rotation rate is (briefly) equal to about 210 rev min-1 (allow ecf of the value from (b))
- For the second mark, accept: answers argued from the shape of an amplitude–driving frequency graph, i.e. the amplitude falls away either side of the peak
During the spin cycle, the drum accelerates from rest to a maximum rotation rate of 1200 revolutions per minute.
The machine vibrates violently, but only for a short time while the drum is speeding up.
Suggest why the machine vibrates violently only for a short time.
Extract:
A washing machine rests on spring mounts. During the spin cycle, the wet clothes in the rotating drum are not evenly distributed, so the drum exerts a periodic force on the machine. The frequency of this force is equal to the rotation frequency of the drum. The machine and its contents can be modelled as a mass–spring system oscillating vertically. The mounts obey Hooke's law.
When marking this question:
- For the first mark, accept: energy is dissipated by (work is done against) the damping force
- For the second mark, accept: the peak of the amplitude–frequency graph becomes lower (and broader)
- Do not accept a bare statement that the amplitude decreases over time — the answer must address the amplitude at resonance
The spring mounts are replaced with mounts containing oil. This increases the damping of the oscillations.
Explain the effect of this change on the amplitude of the oscillations at resonance.