For a spring-mass oscillator, if you triple the mass but keep the stiffness the

Question

For a spring-mass oscillator, if you triple the mass but keep the stiffness the same, by what numerical factor does the period change? That is, if the original period was T and the new period is bT, what is b? It is useful to write out the expression for the period and ask yourself what would happen if you tripled the mass. b = If, instead, you triple the spring stiffness but keep the mass the same, what is the factor b? b = If, instead, you triple the mass and also triple the spring stiffness, what is the factor b? b = If, instead, you triple the amplitude (keeping the original mass and spring stiffness), what is the factor b? b =

Explanation / Answer

T = 2*pi*sqrt(m/k)

a) so tripling the mass add a factor of sqrt(3)=1.73

b) tripling k, factor = 1/sqrt(3)=0.577

c) factors of 3 cancel, so 1

d) doesnt depend on amplitude, so 1

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