Im having a little trouble starting this question(adsbygoogle = window.adsbygoogle || []).push({});

Consider a particle moving without friction on a rippled surface. Gravity acts in the negative [tex]h[/tex] direction. The elevation [tex]h(x)[/tex] of the surface is given by [tex]h(x) = d\cos(kx)[/tex]. If the particle starts at [tex]x = 0[/tex] with a speed [tex]v[/tex] in the [tex]x[/tex] direction, for what values of [tex]v[/tex] will the particle stay on the surface at all times?

There is a picture which shows the curve as a regular cosine wave with period [tex]\displaystyle{T = \frac{2\pi}{k}}[/tex].

Im a little bit unsure on how to go about answering the question. Should i be looking at the forces when the acceleration is a maximum (at the crest of the curve)? And then trying to set up an equation which involves the weight, normal force (which vanishes) and the 'centripetal' force (im not sure of the correct name for this type of force on a cosine wave)

Any help or a hint on how to go about it would be much appreciated.

Thankyou

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# Moving particle

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