Need help with spring mass oscillator and its period

[dayspassingby]

Homework Statement

This is a series of questions about the effect on the period of a spring-mass oscillator when you change the mass, the stiffness, or the amplitude.

(a) 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 and the new period is , what is ? It is useful to write out the expression for the period and ask yourself what would happen if you quadrupled the mass.

(b) If, instead, you quadruple the spring stiffness but keep the mass the same, what is the factor ?

(c) If, instead, you quadruple the mass and also quadruple the spring stiffness, what is the factor ?

(d) If, instead, you quadruple the amplitude (keeping the original mass and spring stiffness), what is the factor ?

Relevant Equations

T = 2pi sqrt(m/k) is the equation for a period

I thought I would multiply b to the whole equation of T, but I have no idea how to formulate into the type of solution it wants

 

[bob012345]

Homework Statement:: This is a series of questions about the effect on the period of a spring-mass oscillator when you change the mass, the stiffness, or the amplitude.

(a) 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 and the new period is , what is ? It is useful to write out the expression for the period and ask yourself what would happen if you quadrupled the mass.

(b) If, instead, you quadruple the spring stiffness but keep the mass the same, what is the factor ?

(c) If, instead, you quadruple the mass and also quadruple the spring stiffness, what is the factor ?

(d) If, instead, you quadruple the amplitude (keeping the original mass and spring stiffness), what is the factor ?
Relevant Equations:: T = 2pi sqrt(m/k) is the equation for a period

I thought I would multiply b to the whole equation of T, but I have no idea how to formulate into the type of solution it wants

This problem is not asking you to solve for the period but to study how it changes when the variables change. $$T = 2 \pi \sqrt{\frac{m}{k}}$$ What happens to $T$ if you change things like the mass $m$ or the stiffness $k$ in the way the problem asks?

 

[kuruman]

With problems like this, if you cannot just look at the expression and figure out the factor, it helps if you (a) write two expressions for the "what happens to" quantity, using subscripts 1 and 2; (b) substitute two different values for the quantity that changes, one multiplied by 1 and the other by the factor it changes; (c) divide the second equation by the first and set it equal to $f$ (for factor); (d) simplify and find $f$. Here is an example.

The area of a circle is $A=\pi R^2$. What happens to the area when you triple the radius?
(a) $~~A_1=\pi R_1^2~;~~A_2=\pi R_2^2$
(b)$~~A_1=\pi (1*R)^2~;~~A_2=\pi (3*R)^2$
(c)$~~f=\dfrac{A_2}{A_1}=\dfrac{\pi (3*R)^2}{\pi (1*R)^2}$
(d)$~~f=\dfrac{\cancel{\pi} ~{9}\cancel{ R^2}}{\cancel{\pi}\cancel{ R^2}}=9.$
Answer: The area increases by a factor of 9.

Do you see how it works? Go for it.