# Two Mechanics Questions 83, 84

1. Nov 30, 2003

### yxgao

There is a diagram that accompanies it so if the explanation isn't clear you can refer to the sample test posted on

the GRE.org website.

83 on GRE. Consider a particle moving without friction on a rippled surface, as shown above. Gravity acts down in the negative h direction. The elevation h(x) of the

surface is given by h(x) = d cos[kx]. If the particle starts at x=0 with a speed v in the x direction, for what values of v will the particle stay on the

surface at all times?

The answer is v <= Sqrt[g/(k^2*d)]
Why, and what concepts are involved here?

84. Two pendulums are attached to a massless spring, as shown above. The arms of the pendulums are of identical lengths l, but the pendulum balls have unequal

masses m1 and m2. The initial distance between the masses is the equilibrium length of the spring, which has spring constant K. What is the highest normal

mode frequency of the system?
A. Sqrt[g/l]
B. Sqrt[K/(m1+m2)]
C. Sqrt[K/m1 + K/m2]
D. Sqrt[g/l + K/m1 + K/m2]
E. Sqrt[2g/l + K/(m1+m2)]