A piston that has a small toy car sitting on it is undergoing simple harmonic motion verti...
A piston that has a small toy car sitting on it is undergoing simple harmonic motion vertically, with amplitude of 5.00 cm, as shown in the figure. When the frequency of oscillation is low, the car stays on the piston. However, when the frequency is increased sufficiently, the car leaves the piston. What is the maximum frequency at which the car will remain in place on the piston?
Step-by-Step Solution
THINK:
To solve this problem, we have to relate the acceleration acting on the car due to piston and acceleration due to gravity. The car will leave the surface of the piston if the acceleration of the piston greater than that of gravity.
SKETCH:
All forces acting on the car is shown below.
RESEARCH:
The position of the object in terms of amplitude can be expressed as
. . . . . . (1)
Differentiating the equation (1) twice with respect to time
, we get the expression for the acceleration of the car as follows
SIMPLIFY:
If net force acting on the car is zero, then the car is in equilibrium on the piston.
The car leaves the piston when 
Net acceleration on the car can be expressed as
. . . . . . (2)
CALUCULATE:
On substituting all values in equation (2), we can calculate the maximum frequency of the piston as
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