Show that vertical oscillation of a loaded spring is simple harmonic.
Answers
Vibration of a particle in Vertical Spring. Consider a light, elastic spring of force constant K. Let its one end be attached to a rigid support such as on ceiling and a mass is attached at the other end as shown in the figure. Hence, the motion of a loaded vertical spring is simple harmonic.
The vertical oscillation on a loaded spring will be stretch and compress for the spring to be beyond with a natural length of the position which is equilibrium for the oscillation process. So to find the loaded spring is very harmonic y=0 and treat as vertical spring for the displacement.
Moreover, from the spring with an image, it will be the position for the right displaced equilibrium position of a spring. When the mass is attached to the left image, the vertical spring-mass system oscillates with equilibrium position y=0
Equation
Ts = 2π√m/k
Whereas Ts is spring period
m is the Mass and k will be the spring constant
Therefore the spring-mass system is directly proportional and inversely proportional to the square root.
