3. 1 points MI4 4.Q.019 My Notes Ask Your Teacher For a spring-mass oscillator,

Question

3. 1 points MI4 4.Q.019 My Notes Ask Your Teacher For a spring-mass oscillator, if you quadruple 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 quadrupled the mass If, instead, you quadruple the spring stiffness but keep the mass the same, what is the factor b? If, instead, you quadruple the mass and also quadruple the spring stiffness, what is the factor b? If, instead, you quadruple the amplitude (keeping the original mass and spring stiffiness), what is the factor b? Additional Materials section 4.1

Explanation / Answer

= (k/m)

f = (1/2) (k/m)

Part a:

if you quadruple the mass but keep the stiffness the same

= (k/m)

replace m = 4m

will be remain halves
b = ½

Part b:

If you quadruple the spring stiffness but keep the mass the same
= (k/m)

Replace k = 4k

will be double

b = 2

Part c:

If you quadruple the mass and also quadruple the spring stiffness
= (k/m)

Replace k = 4k and m = 4m

= (4k/4m)

unchanged
b = 1

Part d:

If you quadruple the amplitude (keeping the original mass and spring stiffness)
= (k/m)
no amplitude in equation, unchanged.

b = 1

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