Does amplitude depend on mass in SHM?

[Mark Zhu]

Homework Statement

Does amplitude of an oscillating spring with an attached block depend on the block's mass? Assuming the spring has spring constant 'k' and obeys Hooke's law. How would the amplitude of the oscillating spring system be affected if the mass of the block were increased/decreased?

Homework Equations

(1/2)mv^2 + (1/2)kx^2 = (1/2)kA^2

The Attempt at a Solution

The amplitude of a spring-block system should depend on the block's mass looking at the conservation of energy equation for SHM. Mass is directly proportional to amplitude.

 

[Charles Link]

If you initially stretch the system by "x" centimeters, which is essentially the amplitude $A$, does it matter what the mass $m$ happens to be? $\\$ How does the system behave if you change $m$ ? e.g. What kind of response does it have if $m$ is very large? What if $m$ is very small? $\\$ I'll give you a hint: The parameter that is affected is the frequency, (how fast it cycles back and forth), usually specified by $\omega=2 \pi f$.