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A weight of 0.12 Newtons stretches a spring by 3 cm. The 0.12 N weight is removed and a 1 Kg mass is attached to the spring. An external force F(t) is provided by a (external) rotating motor and is given by

F(t)=0.04cos(ωt) in Newtons

where the external frequency w can be adjusted. After it reaches the equilibrium position, the spring cannot sustain further elongations larger than 6 cm. The mass is set into motion by the external force F (so at time t=0 the mass is set at rest in the equilibrium position).

Find the spring constant k. Find the internal frequency of the system. Find the motion x(t) of the mass if ω=1.5 and decude the maximum elongation. Find the range of all safe frequencies ω.

Is this the correct ODE for the motion 1/32 x^''+4x=0.04 cos⁡(ωt),where x(0)=0,x^' (0)=1/32

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You asked a very similar question here: math.stackexchange.com/questions/307883/… It was closed because it belongs on physics. You also haven't shown any work-can you find the spring constant? – Ross Millikan Feb 20 at 4:57
That is where I am stuck. I know that the weight is equal to to gravity x mass. and the length is 3 but how to get the length i dont know – DramaFreak Feb 20 at 5:07
Also this question is for an Advanced Differential Equations class thus it is no more math than physics – DramaFreak Feb 20 at 5:08
You could look at Wikipedia under Sinusoidal driving force and set the friction to zero, then see what the amplitude is as a function of the driving amplitude. – Ross Millikan Feb 20 at 5:27
the question has been edited – DramaFreak Feb 21 at 8:45

marked as duplicate by Ross Millikan, Stefan Hansen, Ittay Weiss, JSchlather, Clive Newstead Feb 20 at 11:05

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

1 Answer

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$k$ is the spring constant. Everything else in the question is in MKS so $k \frac N{m}=\frac {0.12}{0.03}=4 \frac N{m}$ The the angular frequency is (this should be in your text) $\omega_0=\sqrt{\frac km}$ You should then have a section on a driven harmonic oscillator. The amplitude has a denominator like $\omega ^2-\omega_0^2$

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What is MKS? We do not have a textbook. – DramaFreak Feb 20 at 5:19
@DramaFreak: meters-kilogram-second, as opposed to CGS, which is centimeter-gram-second. Both are in use and you need to be consistent. The unit of force in CGS is the dyne. – Ross Millikan Feb 20 at 5:22
I know how to figure out the motion but how do i deduce the max elojgation of it? – DramaFreak Feb 20 at 6:43
In the Wikipedia article under Sinusoidal driving force, set the drag term to zero. – Ross Millikan Feb 20 at 13:39

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