I see now. ## \frac {dx_0} {dt} = 0 ## as for each differential time, there is no change in the rest position. This is because rest position is function of where the forces acting on the block are equal only. Right?nasu said:
SHM is a type of periodic motion in which the restoring force is directly proportional to the displacement of the object from its equilibrium position. This results in a sinusoidal or oscillatory motion.
A charged spring mass system can exhibit SHM in an electric field when the charged mass is suspended from a spring and placed in an electric field. The electric field exerts a force on the charged mass, causing it to oscillate back and forth in a sinusoidal motion.
The equation for SHM in this system is given by F = -kx + qE, where F is the restoring force, k is the spring constant, x is the displacement from equilibrium, q is the charge of the mass, and E is the electric field strength.
To prove SHM, we need to show that the restoring force is directly proportional to the displacement of the mass from its equilibrium position. This can be done by measuring the displacement and the corresponding restoring force at different points in the motion and plotting them on a graph. If the graph is a straight line passing through the origin, it indicates that SHM is occurring.
The SHM of this system can be affected by factors such as the strength of the electric field, the mass of the charged object, and the stiffness of the spring. Any changes in these factors can alter the amplitude, frequency, and period of the oscillation.