Analyzing Weight of a Box on an Undulating Road

[Doppler]

The base of compression-type spring balance is rigidly bolted to the floor inside the car.
The spring inside the blance has a spring constant $k=10^4 Nm^{-1}$. box of mass $m=100kg$ is rigidly bolted to the weighing pan of the balance. (The mass of the box is much greater than the mass of the weighing pan, so you may ignore the weighing pan in your analysis.) When the car is parked on a horizontal road, the balance correctly registers the weight of the box, i.e. $980N$

This car is now traveling on a slightly undulating road at a constant horizontal velocity $v$. The profile of the road is shown in figure 2 with $\lambda = 100m$ and $A=1m$. Note that $\lambda \gg A$,and $\lambda$ is much longer than the body length of the car. The shape of this profile may be fitted by a sinosuidal function.

(a) Sketch a graph showing the balance reading $W$, as a function of time $t$, if $v$ is kept constant at $15ms^{-1}$ at all times.
Indicate the time scale on your graph.

(b) Explain clearly how you arrive your answer,giving any derivation if necessary.

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I don't even know how to get start...

 

[Astronuc]

One needs to calculate the natural frequency of the box on the spring.

Then the car driving over a sinusoidal path provides an excitation at what ever frequency that is, which is a function of the speed and wavelength, \lambda.