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AQA Physics A Resonance question

Pleae help anyone,
Q) a vehicle of mass 850kg has a suspension system that is lightly damped. When it is driven without extra load by a driver of mass 50kg over speed bumps spaced 15m apart at a speed of 3ms^-1 , the vehicle resonates.

a) explain why this effect happens
b) AT WHAT SPEED WOULD RESONANCE TAKE PLACE OVER THE SAME SPEED BUMPS IF THE VEHICLE HAD ALSO BEEN CARRYING AN EXTRA LOAD OF 130kg?
(answer. 2.8ms^-1)

i have no clue how to answer part b :frown:

help

Reply 1

Stonebridge

The suspension can be thought of as a spring.
Do you know a formula for the frequency of oscillation of a mass on a spring?
If so, you have the mass (of the car+person) and the frequency of oscillation from the spacing of the bumps and speed of the car.
This will give you k in the formula; the spring constant.
Now increase the mass by 130kg and find the new frequency using the value of k you have calculated.