rude man said:Gravity is always acting and is always constant, so it acts only to set the initial depth, then all other forces are independent of it. In other words, gravity is not a restorative force, and a restorative force is needed to initiate oscillations.
Perhaps an analogous example explains better: consider a spring, constant k, one end attached so as to be immobile, the other attached to a mass m, the whole thing laying on a horizontal frictionless plane. You pull the spring a distance from its relaxed position and it will oscillate back & forth with frequency sqrt(k/m). Gravity not involved.
Now suspend the spring vertically from the immobile end. The spring will stretch due to gravity pulling on the mass to its equilibrium position. Then you pull the spring down a bit further and again it will oscillate with the same frequency sqrt(k/m). The spring-mass system is a lot easier to analyze. You can include gravity or not in your diff. eq.; you get the same result.
Yes, until someone invents variable gravity!Elfrid Payton said:Ah, so only restorative forces are included in differential equations for oscillations, and gravity is never a restorative force?
Buoyancy is the upward force exerted by a fluid on an object that is partially or fully submerged in it. This force is equal to the weight of the fluid that the object displaces. It works because of Archimedes' principle, which states that the buoyant force on an object is equal to the weight of the fluid that the object displaces.
The factors that affect buoyancy include the density of the fluid, the volume of the object submerged, and the gravitational force acting on the object. The more dense the fluid, the greater the buoyant force. The greater the volume of the object submerged, the greater the buoyant force. And the stronger the gravitational force, the greater the buoyant force.
Positive buoyancy is when the buoyant force is greater than the weight of the object, causing it to float. Negative buoyancy is when the weight of the object is greater than the buoyant force, causing it to sink. Objects with a density less than the density of the fluid will experience positive buoyancy, while objects with a density greater than the density of the fluid will experience negative buoyancy.
Buoyancy and density have an inverse relationship. This means that as the density of an object increases, its buoyant force decreases, and vice versa. For example, an object with a lower density than the fluid it is submerged in will experience a greater buoyant force than an object with a higher density than the fluid.
Oscillations, or the back-and-forth motion of an object, do not directly affect the buoyancy of an object. However, the frequency and amplitude of the oscillations can affect the stability of the object in the fluid. If the frequency and amplitude are too great, the object may become unstable and sink due to the increased drag force from the fluid.