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Inertia of a mass spring system

In my textbook it says the frequency of oscillation of a loaded spring is reduced by adding extra mass because this increases the inertia of the system. Could someone please explain exactly how this works? And couldn't you also just argue that increasing the mass reduces the frequency because according to F = ma the acceleration is reduced so speed is reduced so each cycle takes longer?
Reply 1
Avatar for Shaanv
Shaanv
17
Are u familiar with any equations relating frequency, mass and spring constant. If so its easy to see why this happens from a maths-y perspective. There is neat derivations for this formula online.

For oscillations of the same amplitude increasing mass decreases frequency, as the mass has to change direction. but as it has greater mass it has greater inertia so it takes longer for it to change direction from downwards to upwards. So force is lower and acceleration is less.

Im no expert (fellow a level student), trying to put it into words is hard and im not even sure if i an right.

Have u done any experiments on it, it then becomes easy to accept.

Original post by G.Y
In my textbook it says the frequency of oscillation of a loaded spring is reduced by adding extra mass because this increases the inertia of the system. Could someone please explain exactly how this works? And couldn't you also just argue that increasing the mass reduces the frequency because according to F = ma the acceleration is reduced so speed is reduced so each cycle takes longer?
Reply 2
Avatar for G.Y
G.Y
OP
16
Original post by Shaanv
Are u familiar with any equations relating frequency, mass and spring constant. If so its easy to see why this happens from a maths-y perspective. There is neat derivations for this formula online.

For oscillations of the same amplitude increasing mass decreases frequency, as the mass has to change direction. but as it has greater mass it has greater inertia so it takes longer for it to change direction from downwards to upwards. So force is lower and acceleration is less.

Im no expert (fellow a level student), trying to put it into words is hard and im not even sure if i an right.

Have u done any experiments on it, it then becomes easy to accept.


Yes I'm familiar with the formula but was looking for a description of the process as I'm very bad at worded questions and feared it might come up in the exam. Thank you
Reply 3
Avatar for Shaanv
Shaanv
17
Original post by G.Y
Yes I'm familiar with the formula but was looking for a description of the process as I'm very bad at worded questions and feared it might come up in the exam. Thank you


Please take what i said with a grain of salt, its not fact its just my best attempt. 👊🏾
Yeah, newtons second law is just a mathematical statement about inertia... so use F=ma instead of mentioning 'inertia' and it'd be equivalent.

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