Please help with this Harmonic Motion

[don_anon25]

Please help with this! Harmonic Motion

Two masses m1=100 g and m2=100 g slide freely in a horizontal frictionless track and are connected by a spring whose force constant is k=.5 N/m. Find the frequency of oscillatory motion for this system. I know omega = sqrt (k/m), but I have two masses, rather than just one. How does this work? Could someone give me an idea of how I should go about solving this?

Thanks!

 

[lightgrav]

there's a place in the spring which doesn't move (the center-of-mass).
so each side of the spring stretches independently, with a new k.

 

[quicknote]

I would be more than happy to assist you with this problem. In order to find the frequency of oscillatory motion for this system, we can use the equation for the natural frequency of a mass-spring system, which is given by f = 1/2π √(k/m). In this case, we have two masses (m1 and m2) connected by the same spring with force constant k.

To find the frequency, we can consider the system as one effective mass (m1+m2) connected to the spring. This is because the two masses are connected by the same spring, and their motion will be in sync due to the spring's elasticity. Therefore, we can use the effective mass (m1+m2) in the equation for natural frequency.

So, the frequency of oscillatory motion for this system will be f = 1/2π √(k/(m1+m2)). Plugging in the given values, we get f = 1/2π √(0.5/(0.1+0.1)) = 1.59 Hz.

I hope this helps you understand the concept of finding the frequency for a system with two masses connected by a spring. If you have any further questions, please do not hesitate to ask. Keep exploring the fascinating world of harmonic motion!