Spring constant question

"Dr Nasty hates the laundry. She designs 40kg washing machines which resonate when they spin the clothes. Her machine spins at 1200 rpm and when it resonates, it lurches about in the kitchen, putting holes in the cupboards and making a lot of noise. Calculate the 'spring constant' she designs the machines to have in order to achieve her horrible plan"

I got this from the IsaacPhysics booklet thing, and im kinda confused as to how I should start the question.

Reply 1

username3346672

10

Okay, so at 1200 rotations per minute there is resonance. So therefore the resonant (natural) frequency of the washing machine f is 1200/60. F = -kx and if we’re talking about natural frequency we wanna think about simple harmonic motion the -kx = -mw^2x . The -x cancels, leaving k = mw^2 . As w = 2pi f k = m(2 pi f)^2 . So the spring constant will equal 631654 N/m which seems large so I might’ve gone wrong somewhere, let me know what the correct answer is

Reply 2

TheJazzPhysicist

13

Original post by JR127

Okay, so at 1200 rotations per minute there is resonance. So therefore the resonant (natural) frequency of the washing machine f is 1200/60. F = -kx and if we’re talking about natural frequency we wanna think about simple harmonic motion the -kx = -mw^2x . The -x cancels, leaving k = mw^2 . As w = 2pi f k = m(2 pi f)^2 . So the spring constant will equal 631654 N/m which seems large so I might’ve gone wrong somewhere, let me know what the correct answer is

A year late, but that's correct lol

Reply 3

lifeofpablo1

14

you just equated force and acceleration how does this even work

Original post by JR127

Okay, so at 1200 rotations per minute there is resonance. So therefore the resonant (natural) frequency of the washing machine f is 1200/60. F = -kx and if we’re talking about natural frequency we wanna think about simple harmonic motion the -kx = -mw^2x . The -x cancels, leaving k = mw^2 . As w = 2pi f k = m(2 pi f)^2 . So the spring constant will equal 631654 N/m which seems large so I might’ve gone wrong somewhere, let me know what the correct answer is