cheimdal said:Homework Statement
A marble is oscillating in a parabolic bowl ( y = ax^2 ) Assuming mechanical energy is conserved, and that the oscillation amplitude is small, find the oscillation frequency.
(Use the potential energy to find the force acting on the marble as a function of x)
Homework Equations
Well obviously EP = mgy = mgax^2
small oscillations: sin t can be approximated by t.
I can't figure out how to put up the differential equation correctly.
A parabolic bowl is a curved surface in the shape of a parabola, which is a type of conic section. It is created by rotating a parabola around its axis.
Marble is often used in parabolic bowls as it is a smooth, round object that can roll easily along the surface of the bowl. It can also be used to demonstrate the properties of a parabolic shape, such as focusing light or sound waves.
When a marble is placed in a parabolic bowl, it will roll towards the center of the bowl due to the force of gravity. As it reaches the bottom of the bowl, it will then roll back up towards the rim, creating a continuous motion.
The shape of a parabolic bowl causes the marble to follow a curved path, rather than a straight line. This is because the bowl's curved surface creates a gravitational pull towards the center, causing the marble to change direction as it rolls along the surface.
Parabolic bowls have a variety of applications in different fields, such as in satellite dishes, solar cookers, and parabolic microphones. They are also commonly used in physics experiments to demonstrate the properties of a parabolic shape.