Help please -- Amplitude of a spring - does it change with mass?

[Izzy Levine]

Hello! In some of my college Physics practice problems, amplitude of a spring in Simple Harmonic Motion does not change with mass (for example, when the mass splits in 2 at equilibrium in a horizontal oscillator - see picture). But, in other problems, the Vmax of the oscillator remains constant with changing mass while A changes. Which is true? Is amplitude independent of mass or not? And for velocity?

Thanks! (Exam is tonight, SOS!)

 

[russ_watters]

Welcome to PF!

Hello! In some of my college Physics practice problems, amplitude of a spring in Simple Harmonic Motion does not change with mass (for example, when the mass splits in 2 at equilibrium in a horizontal oscillator - see picture). But, in other problems, the Vmax of the oscillator remains constant with changing mass while A changes. Which is true? Is amplitude independent of mass or not? And for velocity?

Thanks! (Exam is tonight, SOS!)

This is going to depend on the specifics of the problem. Often, amplitude is ignored or given, because the more interesting changes are to period. For a real-world system, how amplitude is affected will depend on how the system is set in motion. Eg, is amplitude specified? Force? Energy? Speed?

In this problem, the energy is input and the equilibrium speed is the bridge between the before and after scenarios.

 

[tech99]

Hello! In some of my college Physics practice problems, amplitude of a spring in Simple Harmonic Motion does not change with mass (for example, when the mass splits in 2 at equilibrium in a horizontal oscillator - see picture). But, in other problems, the Vmax of the oscillator remains constant with changing mass while A changes. Which is true? Is amplitude independent of mass or not? And for velocity?

Thanks! (Exam is tonight, SOS!)

The two cases you quote are equivalent to an electrical LC circuit where the generator either inserts a specified current in series with LC or applies a specified voltage across L and C in parallel.
In the first case, the defined current creates a large voltage across L and C. And in the second the defined voltage creates a large current in both L and C.
In your mechanical examples, if we first deflect the spring a finite amount, that is like charging the capacitor, and the amplitude (voltage) will never exceed this again. On the other hand, if you give the mass a velocity, that is equivalent to inserting a current in series with L and C and the current (velocity) will never exceed that value.
So it depends how you drive the oscillator and of course, as mentioned by russ_watters, it depends whether the question defines the force or speed of the generator or the energy stored in the system.

 

[Tom Hammer]

I think this is easiest solved using energy. Potential energy (PE) of the spring when compressed at (b) = KE of both objects at (c) = PE of spring + KE of sliding object in (d)