A. For a spring-mass oscillator, if you double 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 b⁢T, what is b? It is useful to write out the expression for the period and ask yourself what would happen if you doubled the mass. b. If, instead, you quadruple the spring stiffness but keep the mass the same, what is the factor b?c. If, instead, you quadruple the mass and also quadruple the spring stiffness, what is the factor b?d. If, instead, you quadruple the amplitude (keeping the original mass and spring stiffness), what is the factor b?

a) factor

b) factor

c) factor

d) factor

Explanation:

Time period of oscillating spring-mass system is given as:

where:

frequency of oscillation

mass of the object attached to the spring

stiffness constant of the spring

a) On doubling the mass:

Then the new time period:

where the factor as asked in the question.

b) On quadrupling the stiffness constant while other factors are constant:

New stiffness constant,

Then the new time period:

where the factor    as asked in the question.

c) On quadrupling the stiffness constant as well as mass:

New stiffness constant,

New mas,

Then the new time period:

where factor as asked in the question.

d) On quadrupling the amplitude there will be no effect on the time period because T is independent of amplitude as we can observe in the equation.

so, factor