Question: What is the Effect of Mass on SHM Acceleration?

[Peter G.]

Hi,

I have a question:

What happens when: We add increase the mass on a spring, displace it as much as we did with a lighter mass and allow it to oscillate. Would the period remain the same? In the end, the force was increased when displacing and the maximum displacement was kept constant.

Thanks

 

[Doc Al]

Ask yourself: What determines the period of a mass on a spring?

 

[vela]

In the end, the force was increased when displacing and the maximum displacement was kept constant.

This isn't correct. What law describes the force exerted by a spring?

 

[Peter G.]

Doc Al: The mass and the spring constant determine the period?
Vela: Hooke's Law describes the force exerted by a spring (product of the spring constant and extension until the elastic limit)

I was also thinking... (This is also probably wrong but you guys can maybe help me get over it) If the mass increases for the same force therefore the acceleration must decrease.

According to a = -w²x

The period must increase or the displacement decrease and the period remains constant. That is, the amplitude would be decreased so a full cycle would cover a smaller length...

 

[Doc Al]

Doc Al: The mass and the spring constant determine the period?

Right. Note that period does not depend on displacement.

Vela: Hooke's Law describes the force exerted by a spring (product of the spring constant and extension until the elastic limit)

Right. Note that force depends on spring constant and displacement, not on the mass.

I was also thinking... (This is also probably wrong but you guys can maybe help me get over it) If the mass increases for the same force therefore the acceleration must decrease.

Makes sense to me.

According to a = -w²x

That's good.

The period must increase or the displacement decrease and the period remains constant. That is, the amplitude would be decreased so a full cycle would cover a smaller length...

Since you gave the mass the same initial displacement, the amplitude is the same. But, since you changed the mass, the period changes. Since, as you point out, the acceleration is less at each point, it takes longer for the mass to go through its cycle: The period increases.

 

[Peter G.]

Since you gave the mass the same initial displacement, the amplitude is the same. But, since you changed the mass, the period changes. Since, as you point out, the acceleration is less at each point, it takes longer for the mass to go through its cycle: The period increases.

Ok, cool. Just one last thing. Using the same example if we reduce the initial displacement is it possible that we keep the period the same?

 

[Doc Al]

Just one last thing. Using the same example if we reduce the initial displacement is it possible that we keep the period the same?

You tell me. Does the period depend on the initial displacement?

 

[Peter G.]

Nop, it does not.