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I think it's just a sloppy and misleading way to describe the direction. Note how they 'derive' the inertia force: It's just the negative of 'ma'.jason.bourne said:it has been mentioned in this website that 'inertia force acts opposite to the direction of motion'.
did i understand it right?
Since your variable x already defines the positive direction of acceleration, x¨, the inertia force is simply −mx¨
[itex]\ddot{x}[/itex] is positive as long as the acceleration is in the positive direction, which you have defined as downward. Note that the restoring force of the spring always acts to accelerate the mass back towards the equilibrium point. So at any point below the equilibrium point, the acceleration would be upward.jason.bourne said:as i defined downward x as positive, so does that mean x¨ is positive as i move downwards away from equilibrium?
You wouldn't put the acceleration on a free body diagram, but it would act upward.i might be asking really very silly doubt but this thing is really confusing me. i want it to be sorted.
as the mass moves away from equilibrium towards +A in the downward positive x direction, if we draw a free body diagram, how do we represent acceleration?
[itex]\ddot{x}[/itex] would be negative and the inertia force would be positive. But you don't have to worry about the inertia force direction--you'd still represent that inertia force as [itex]-m\ddot{x}[/itex].if we take x¨, acceleration positive in the downward direction, the inertia force acts in the opposite direction i.e, upwards.
Right.so if i write equation of motion using D'Alembert's Principle, i get:
-mx¨ - kx = 0.
So now you are looking at the situation when the mass is above the equilibrium point. So the spring force acts downward and the acceleration is downward.but if i consider the situation where the mass is at a position, away from -A, towards equilibrium, then what is the direction of acceleration and how do i write the equation of motion?
The equation of motion for a spring mass system is given by F = ma, where F is the force applied to the mass, m is the mass of the object, and a is the acceleration of the object.
A free undamped vibration is the natural oscillation of a spring mass system without any external forces or damping present. This means that the system will continue to vibrate at its natural frequency indefinitely.
The natural frequency of a spring mass system can be calculated using the equation f_{n} = √(k/m), where k is the spring constant and m is the mass of the object. This represents the frequency at which the system will naturally vibrate without any external forces.
The amplitude of a spring mass system's vibration refers to the maximum displacement of the mass from its equilibrium position during one full cycle of oscillation. It is affected by factors such as the initial conditions and the energy applied to the system.
The spring constant and the natural frequency of a spring mass system are directly proportional. This means that as the spring constant increases, the natural frequency of the system also increases. This can be seen in the equation f_{n} = √(k/m), where a higher spring constant results in a higher natural frequency.