Almost. F = - dU/dx. (You just forgot the minus sign.)gipc said:Well, I guess F=10x-10
Sure, but it's the same differential equation as for any simple harmonic motion. I assume you know the solution by heart or can look it up. If you knew the spring constant and the mass, could you find the period?Doesn't there has to be some differential equation involved?
Doc Al said:I assume you know the solution by heart or can look it up
Simple harmonic motion is a type of periodic motion in which the restoring force is directly proportional to the displacement from equilibrium. This means that the object will oscillate back and forth along a straight line, with its maximum displacement at the ends and its equilibrium position at the center.
The period of a simple harmonic motion is the time it takes for one complete cycle. It can be calculated by using the formula T = 2π√(m/k), where T is the period, m is the mass of the object, and k is the spring constant of the system.
The frequency of a simple harmonic motion is the number of cycles per unit of time. It is inversely proportional to the period, meaning that as the frequency increases, the period decreases. This relationship can be represented by the formula f = 1/T.
The amplitude of a simple harmonic motion is the maximum displacement of the object from its equilibrium position. It does not affect the period or frequency of the motion, but it does affect the maximum velocity and acceleration of the object. A larger amplitude will result in a greater maximum velocity and acceleration.
In simple harmonic motion, there is no external force acting on the system, and the motion will continue indefinitely. In damped harmonic motion, there is an external force (such as friction) that causes the oscillations to gradually decrease in amplitude and eventually come to a stop. Damped harmonic motion is a more realistic representation of real-world systems, while simple harmonic motion is an idealized concept used in physics calculations.